Not a straw man at all!
And no, not everyone can make the choice to use it. There simply isn't enough space, and if everyone drove then traffic would be horrendous. In Manhattan only 1 in 5 people even own cars, for example, and yet on-street parking is always completely full everywhere. So it doesn't make sense to offer it for free given that most people cannot use it. People who don't use it should not be paying for it and people who do use it should be paying their fair share.
Regarding 1 in 5 people own a car, that I think pretty much works out to full parking everywhere, since the area of the street available for parking is definitely not 1 per capita, but probably way less.
I can also apply your logic to school system. Why am I paying school taxes if I don't have children?
no passenger seat or they all sit behind you in single file?