Not really. I finish all of my games by turn 300 on Emperor difficulty and to get all of those districts you only need at 13 pop city. Its going to have to be an early city to do that but its totally possible to do if know what you are doing. The inspiration for
Urbanization, an Industrial era civic, is to have a 15 pop city so its not an impossible thing to do by the late mid-game, ignoring the fact that airports are a late game tech. Build farm triangles in your cities and use internal trade routes to help grow your cities and its possible to do. But, you shouldn't need to do that anyway. Have a couple of cities dedicated to military unit production(Encampment, Industrial Zone, and Commercial Hub[if you want]) and then a couple of other cities focused on generating science, culture, and gold (Campus, Theater Square, and Commercial Hub/Harbor). All of your cities are not going to be able to everything and specializing is a totally valid thing to do.