If taxes on cars were to increase for infrastructure, it would feel like the government is double dipping. Not to mention the general benefit in infrastructure for society as a whole. The benefits for economy can't be understated, not to mention the increased taxes you get across the board.
It's actually quite uncommon to see free government-owned parking lots where I live and when you do see it it's usually a loss leader to encourage people to visit local retailers (where the government will make its money back through sales taxes, income taxes, fuel taxes, encouraging jobs so unemployment, etc).
There are a couple of exceptions like cigarette taxes and I now believe some of the emissions tax all vehicles pay has been ear marked for roads - though I'm not a fan of this (and a cyclist) as it leads to the feeling that car drivers 'own' that road as they 'pay' for it.
Remember, the side effect of this policy is that car ownership rate becomes really low. I doubt the purpose is to increase revenue. Maybe it's more about minimizing the negative externalities.
Anyway, I don't think it's a ban. There are literally cars in Singapore :) If you think a regular sedan is worth >$100k (it's normal in Singapore), you can buy it. But make sure you pay for the externalities (traffic, pollution, parking, road-building, ...) that is caused by your choice.