I've seen this sad downward spiral multiple times, it is not a good outcome.
I used to live not too far from a town with a mellow but nice downtown center. Not a huge draw but many small nice restaurants and shops and there was steady business. Sensing a profit machine, the city filled all streets with parking meters. Turns out that while it was a nice area, it wasn't so irreplaceable, so nobody goes anymore. Business collapsed. I drove by last summer and everything is closed, the parking meters sit empty.
Same is happening now to the downtown one town over. It used to very vibrant awesome downtown, although small. Bars, restaurants, music venues, fun shops. I was there every night for something or other. Loved it. Easy free parking around. Some of the parking lots have office buildings now and the city lots have become very expensive. Much less activity there now, about a third of the venues are closed and the remaining ones are saying they can't last very long with fewer people going. While in its heyday this downtown was far more active than my first example, turns out it wasn't irreplaceable either. People just don't go anymore.
Point is that this tactic works only when the downtown is so established and so dense that people are going to go anyway even if parking is hard, like Manhattan.