This is why the residential areas should also not have free parking. If you want to privatize a public resource, space in this case, you should pay an appropriate price to reflect the fact that you are doing so.
Space which gets more expensive with density right? The density that you're trying to increase. This just makes it illegal for poor to middle class people to have cars.
No, it just means that if you don't need parking you don't have to pay for it. And reducing parking requirements makes it easier to not need a car (and thereby parking) which is great if you're poor to middle class.