It's a tragedy of the commons issue, which is something the free market is known not to be able to handle.
Paying for parking only works in places where you park temporarily and then move elsewhere, you can't exactly add meters in front of people's homes, unless, I suppose every house had off street parking?
I guess that's one way to have a city. Something similar is done by making overnight street parking illegal - I've seen that a lot, and then yes, the free market will make sure every house has its own parking area.
It's hard on visitors though.
Parking minimums are actually the least bad option from all of those.
Regardless, the consideration needs to take into account that requiring parking minimums increases cost to develop and decreases density, making it harder to live without a car. If it were a given that everyone has a car and drives it everywhere, I think indeed it probably does make sense to have (reasonable) parking minimums and I think it's clear that parking minimums do certainly make for ample parking. But in today's world where we are trying to shift away from car primacy in cities because they are dangerous and polluting and scale poorly, the goal shifts from "make there be enough parking" to "make it easy to get around the city" and for that goal, parking minimums have proven to be ineffective.
Serious question: why not?
I loathe the idea, personally, of yet more rent, but I'm having a tough time refuting the parent comment myself.
You're trying to avoid people using on-street because they didn't build off-street. But even if a minimum build is required, it seems to me that people would still prefer utilizing the on-street parking? As it is free, assuming the landlord charges for off-street, and why wouldn't the landlord charge? (Mine does; that's a $70/mo incentive to park on-street. Our garage is, unsurprisingly, mostly empty.)
(The whole thing seems horridly regressive, given the requirement for transportation; even though I'm technically in a major megalopolis, I cannot cut a car from my life for a variety of reasons which amount to "sufficient services are not accessible by public transit". I prefer public transit, when I can, but I cannot 100% of the time.
Also, sometimes travel, and renting is absurdly expensive.)
(Like, ultimately, the landlord is never going to utilize the build spaces fully if he believes that an increased price will fetch more $ overall, even if some spaces are then unused. Or worse, we get price discrimination, possibly due to information asymmetry in the pricing. Those forced out are probably then using on-street.)
I anticipated your question and answered it in my next paragraph. You can do it if you want, but you have to start the city that way. Instead of money you do it with overnight parking restrictions, it ends up the same.
Personally I find it to be a worse solution. And the rest of your message talks about some of the reasons why.
Parking minimums are just better.