If you want to build apartments and homes in Nashville, you are required to build parking for cars. Otherwise, the city council will kill your project.
Changing rules for parking generally serves only to create local parking shortages (and subsequent emotional discussions) as rhetoric underlying problem is not addresssed. This is a bit chicken-and-egg, but consider what happens if a standard subdivision is built without driveways, parking lots, or garage space. A 2 mile walk to the grocery store doesn’t really work. Instead, the regulations should be for higher density, space for bicycles (and transit), and space for essential amenities like small, local grocery stores and restaurants. ETA - with current conditions creating unplanned multigenerational housing, dad, mom, kid1, kid2, and partners makes for tight parking even with 3 spots.
You know, like they used to build before it was about maximizing the revenue per square mile of land?
Are you conflating the idea of banning parking with repealing mandatory parking? These are two very different policies. Developers will still build parking infrastructure when the market demands it and it makes sense for the neighborhood and project. They just won’t be universally required to even when literally no one wants it.
It’s not always the case that builders provide parking. The market demands shareholder profits, and if you don’t build a driveway, that’s more units you can fit on a given plot of land.
This is the trend I’m observing, but I’m certain it is not universal. 
Parking is for residents. If they want more parking, they can pay for a property that has that, which will usually cost more. If not, they can pay less and go without. This is a good thing and it’s not something the government needs to involve itself in. Right now the vast majority of places (in the US at least) have a really excessive amount of parking, so it may be that segment of the market is temporarily saturated, and they’re building for a market that wants less, which has gone unserved for a long time due to these pointless laws.