Sounds like a big job, just like many big city mayors, but with certain services carved out for the cities to provide themselves in incorporated areas.

Wikipedia:
https://en.m.wikipedia.org/wiki/Miami-Dade_County,_Florida

"Miami-Dade County has operated under a unique metropolitan system of government, a "two-tier federation", since 1957. This was made possible when Florida voters approved a constitutional amendment in 1956 that allowed the people of Dade County (as it was known) to enact a home rule charter. Prior to this year, home rule did not exist in Florida, and all counties were limited to the same set of powers by the Florida Constitution and state law.

Unlike a consolidated city-county, where the city and county governments merge into a single entity, these two entities are separate. Instead there are two "tiers", or levels, of government: city and county. There are 34 municipalities in the county, the City of Miami being the largest.

Cities are the "lower tier" of local government, providing police and fire protection, zoning and code enforcement, and other typical city services within their jurisdiction. These services are paid for by city taxes. The County is the "upper tier", and it provides services of a metropolitan nature, such as emergency management, airport and seaport operations, public housing and health care services, transportation, environmental services, solid waste disposal etc. These are funded by county taxes, which are assessed on all incorporated and unincorporated areas.

Of the county's 2.6 million total residents (as of 2013), approximately 52% live in unincorporated areas, the majority of which are heavily suburbanized. These residents are part of the Unincorporated Municipal Services Area (UMSA). For these residents, the County fills the role of both lower- and upper-tier government, the County Commission acting as their lower-tier municipal representative body. Residents within UMSA pay a UMSA tax, equivalent to a city tax, which is used to provide County residents with equivalent city services (police, fire, zoning, water and sewer, etc.). Residents of incorporated areas do not pay UMSA tax."