[kelnos]

Because public transit is woefully inadequate to get people where they need to go in nearly every city in the US. Even if we were to magically immediately fund this to the levels needed, it would take 10-20 years to build out that infrastructure. (To be fair, need could be met with buses until subways and other light rail is built.)

But people in the US don't actually want that, unfortunately. They mostly like being able to drive around in cities (either their own city, or nearby cities where they want to visit). It's weird to say that, because most people would probably say they hate driving in city traffic. But when the alternative is driving to some sort of park-and-ride and switching to trains or buses, many US residents will prefer to drive.

Let's also not forget that even some of the most transit-heavy places in the world still allow private vehicles. In some (Tokyo especially comes to mind), it ends up usually being more expensive and take more time to drive than to take transit, but people still choose or need to do it for whatever reason.

Your phrasing of "why cities allow" is a common one, but remember that a city isn't its own entity with its own wants and desires. The laws reflect the wants and desires of the voters who live there.