When two hijacked jetliners struck the World Trade Center towers in New York City on the morning of Sept. 11, 2001, Mayor Rudolph Giuliani became the face of a city struggling with tragedy, a ubiquitous presence projecting authority, assurance and control. The reputation he forged that day would be tarnished with time, but it became a model for mayors facing crises across the country.

As Mayor Karen Bass of Los Angeles confronts a city dealing with devastating fires, her performance has raised questions, even among her supporters, about whether she can become the dominant executive leading a city through a crisis that New Yorkers saw more than 23 years ago.

Some of those concerns reflect her relative lack of executive experience — she is a former member of Congress and the California assembly, where she served in the powerful role of speaker. And some of those concerns have to do with the fallout from her absence from the city when the fires broke out.

But the question of who is in charge — of who is playing the role in Los Angeles that Mr. Giuliani did in New York, to use one example — is also testimony to the diffusion and, at times, dysfunction that make up the core DNA of the governance of the greater Los Angeles area. That muddled authority is a sharp, and by design deliberate, contrast with New York, Philadelphia, Chicago and other cities that are dominated by powerful, high-profile mayors.

The city of Los Angeles, with a population of 3.8 million, is one of 88 different cities that make up the county of Los Angeles. That county, with a population of 9.6 million spread across 4,751 square miles stretching inland from the Pacific Ocean, is controlled by a five-person board of supervisors, each one representing 1.9 million people. Each of those supervisors rivals the mayor of Los Angeles in clout as they oversee their own fiefdoms in the nation’s most populous county, even if they are relatively unknown by constituents.

Within those vast borders, there is a Los Angeles Police Department and a Los Angeles County Sheriff’s Department, as well as an additional 45 police departments protecting, to name a few, Santa Monica, Long Beach, Inglewood and Pasadena. There are dozens of municipal fire departments, including one that serves the city and another that serves the county.

One of the two major fires that devastated this region — the Eaton fire — is not even in the city of Los Angeles; it is in an unincorporated section of Los Angeles County. The response to the Eaton fire was led by the county fire department; the city fire department was at the forefront in fighting the Palisades fire.

All of this is a recipe, analysts said, for rivalry among elected officials and confusion among voters, and a challenge for even the most accomplished elected official trying to grab the mantle of leadership amid what Gray Davis, a former California governor, called “the dispersed and discombobulated nature of our government.”

“As an executive most of my life — controller, lieutenant governor, governor — there’s a time when you need clear accountability, someone who will give orders and accept responsibility whether things work or not,” said Mr. Davis, who served as governor from 1999 to 2003. “The public here seems not to want that on a day-to-day basis. But when there is an emergency, we need that. And we don’t have that system.”

When New Orleans was overrun by Hurricane Katrina in 2005, resulting in devastating damage and hundreds of deaths, the mayor, C. Ray Nagin, stepped forward to lead his city through the crisis, and to raise his national profile. (Mr. Nagin’s reputation, like Mr. Giuliani’s, also faded with time.) At a recent press briefing about the fires in Los Angeles, eight city and county officials lined up to speak. Ms. Bass was just one part of the lineup, talking about the Palisades fire, but so was Kathryn Barger, the increasingly high-profile member of the county board of supervisors whose district includes the Eaton fire.

“What you have in a city like New York is a fundamentally mayor-oriented system where, even in quiet times, everything flows to the mayor,” said Raphael J. Sonenshein, a longtime expert on Los Angeles politics and government and the executive director of the Haynes Foundation, a Los Angeles civic research organization. “Here it’s a little more of an art to exercise mayoral leadership. The mayor might have strong opinions, but to get problems solved, you have to figure out how to get these governance agencies to work together. It’s very hard to get things done.”

None of this is accidental.

The web of overlapping governments is the product of a reformist system of governance that has evolved over the years, designed to constrain the authority of cities, counties and the people who lead them. Many of the people who settled here over the past century came from the Midwest, and they carry a strong distrust of the powerful mayors and political machines found in cities like Philadelphia, New York and Chicago.

The mayor of Los Angeles does not control the school system, as is the case in some other large cities. Public health falls mostly under the jurisdiction of Los Angeles County, forcing the mayor and supervisors to work together on challenges such as homelessness. In the city, there is a police commission that makes the final decisions on hiring and firing police chiefs; Ms. Bass needs the commission to ratify her choice of who should head the department.

The stakes here are high. The fires are diminishing, but rebuilding could end up being as challenging as battling the fires, testing the resources and agility of this teeming catalog of elected officials.

Eric M. Garcetti, a former mayor, said all these government agencies — notwithstanding any history of rivalry — had appeared to work in tandem as the fires raged. “But for the rebuild, it’ll be absolutely critical for us to act like we’re one city and not a collection of 88 villages,” he said in an interview from India, where he is now the U.S. ambassador.

These structural tensions have long been a source of frustration for Los Angeles mayors. In interviews, two of them — Mr. Garcetti and Antonio Villaraigosa — said they would support creating a dominant government representing the region, to replace the network of overlapping municipal governments. Mr. Villaraigosa said he supported, for example, remaking Los Angeles along the lines of San Francisco, which is both a county and a city. They both argued the issue had become more urgent with the kind of natural disasters that have come with climate change.

“I don’t think that’s going happen in my lifetime, but it would certainly make things more coherent,” Mr. Garcetti said. For now, he said, mayors have to fall back on the power of persuasion. “Informal power is so critical,” he said. “It is so critical to put together coalitions.”

Mr. Villaraigosa said that, in raising concerns about the structural challenges Los Angeles faces, he was not criticizing Ms. Bass. “I don’t want to join that,” he said. “But when you have all agencies involved — 25 people speaking — it diffuses the leadership model. You have two different bureaucracies trying to work together. Sometimes they do, sometimes they don’t.”

By contrast, unconstrained by jurisdictions, Gov. Gavin Newsom has been an ever-present figure over these past nearly two weeks, walking through smoky ruins as he has talked with firefighters and people who have lost their homes. He expanded a special legislative session to address the Los Angeles wildfires and signed executive orders dealing with response and recovery efforts.

Ms. Bass has been criticized for being out of the country when the fires erupted — she was in Ghana in West Africa to attend the inauguration of its new president. Upon her return, in a widely circulated clip, Ms. Bass stood silently as a reporter pressed her on why she left amid warnings of dangerous fire weather.

Since her return, she has issued her own executive orders to expedite rebuilding, and she has named a longtime civic leader, Steve Soboroff, to head recovery efforts. But she has also repeatedly defended her performance, saying that she and leaders across the region are working “in lock step” to address the crisis.

“We are actively fighting this fire,” she said at a news conference on the second day of the crisis, adding: “So what we are seeing is the result of eight months of negligible rain and winds that have not been seen in L.A. in at least 14 years. And we have to resist any — any — effort to pull us apart.”

The mayor’s office did not immediately return a request for comment on Saturday.

Even before the fire, there was movement to repair the system. In November, county voters endorsed the biggest change in its government in a century — including the establishment of a new person to lead the county of Los Angeles, an elected county executive who will be chosen in the 2028 election.

“They will be the most powerful elected official in the United States,” said Fernando Guerra, the head of the Center for the Study of Los Angeles at Loyola Marymount University. “They will represent 10 million people. They will have a lot of power. Most important, they are going to steal the thunder and the pulpit from the mayor of Los Angeles. It’s going to be as centralized as New York is now.”

It’s difficult to say what role a county executive might have played in directing the government’s response to the fires, a duty typically overseen by the fire departments themselves. But officials said that what the region needed, in addition to the fire and police officials who directed the response, was a political leader displaying moral authority and leadership, with the platform to speak across the expanse of a county whose population is larger than that of most states.

“People want to see their elected official — they want to see who is in charge,” said Zev Yaroslavky, who spent 20 years as a member of the Los Angeles City Council and 20 years as a member of the Los Angeles County Board of Supervisors. “In this particular case, the fact is you had two different big fires: one in the city of Los Angeles and one in the unincorporated area of the county. Who is in charge?”

Shawn Hubler contributed reporting.