It's more like the other way around: the idea is to make public transport cheap and efficient enough that it's a reasonable alternative to driving everywhere.
>> For example I live in a very public transit friendly city, but the buses are un-ridable most of the time due to the rampant homeless issue(and all that comes with a large homeless population) while the light rail is usually better about being a semi-safe, semi-clean environment, that just happens to be so overloaded between between 7am-9am, and 3pm-6pm, that there is almost any price I'd pay to avoid it.
I live in a small town on the South coast of England, which just happens to have one of the largest populations of homeless people, nationally. It also has very good public transport, namely, buses, that are always full. I've never seen a homeless person using a bus as crashing space, or causing trouble of any sort. I can't say I ever particularly noticed homeless people on a bus. If homeless people on buses are a problem where you live, that has nothing to do with public transport in general.
Anyway, I think everyone gets the public transport they deserve. If everyone wants to go around by car, then we won't have good public transport- because why would we?