They don't solve anything
If everyone had flying cars, there would be regulations to them, including not being able to just go anywhere, and specially there would be 'air roads' meaning there would still be traffic jams and the like; And in general we would need completely new systems and infrastructure, electric cars are nothing new and they still are not that usable on some places, imagine with flying cars.
Unless we get some new fancy engine and fuel storage, having a machine made to fly long distances is simply not feasible while being in the same footprint and having the same features of a car, they would either have the same 'luxuries' as a car (air conditioners, 5 seats, etc) and have extremely low range, or having almost anything and a low carrying capacity.
If you need to fly long distances, planes already exist.
If you need to go to some specific spot in the city, helicopters already exist.
And overall, a few public and shared transport vehicles > many personal transport vehicles.
They are dangerous
Unless every flying car is part autogyro, having any mechanical issue means falling to your death or heavy destruction.
Also, piloting one of these would require basically a plane license anyway, or you can make them be mostly computer controlled and have any glitches also easily cause deaths.
btw, new Helluva Boss episode. Moxxie still adorable!