In a recent interview, Mr. Taylor recalled meeting with Mr. de Blasio about taking the job. “It was about hearts and minds, the importance of the work,” he said.

Around the time Mr. de Blasio took office, The New York Times published a series of articles about Dasani Coates, an 11-year-old girl, and her family living in squalid conditions in the city’s shelter system. Children and families remain the bulk of the city’s homeless population and the largest group living in the city’s shelters, and Mr. Taylor’s expertise in dealing with such families was part of his appeal.

But the most visible part of the problem is on the streets — mostly single adults and people, some homeless, some not — who panhandle in very public places, mostly in Manhattan.

Mr. Taylor faced one challenge after another, including removing children from the Brooklyn shelter where Dasani and her family had stayed and an inquiry by the city’s Investigation Department into shelter conditions. “It was very, very intense,” he said of his early months as commissioner.

Advocates for homeless people and leaders in the union that represents shelter workers described Mr. Taylor as a skilled manager who visited shelters in the early morning so he could see how children were getting to school and at night so he could review overnight intakes. They said he had inherited the crisis, which began escalating in 2011 after the state cut funding for rental assistance programs.

Some advocates, however, said he was an inexperienced leader who had difficulty supervising staff and navigating the political landscape.

After the three-term tenure of former Mayor Michael R. Bloomberg, a political independent, shelter and housing providers appeared to be looking for institutional knowledge. They found that in Mr. Banks, formerly a top attorney with the Legal Aid Society who spent more than three decades fighting the city on homelessness.