This happens in some part of downtown here, mainly the business district. It's dead during any part of the day other than noon on weekdays. The reason isn't high fees, it's just that it's a boring part of the city center where there's nothing to do and it's very very car focused. Not a lot of interesting places can sustain by catering to cars. Every other part that isn't infested with cars is vibrant with life at any time of day. Raising parking fees, removing parking and removing car trafic has the opposite effect : it makes it so that the city center stops suffocating under cars.

Unfortunately, the idea of the city center being sustained by suburbs with cars is just a myth. It's mostly strangled by them in most north american cities. It can sustain on it's own by catering to the population that lives in them or close by. And if there's not enough population, densify. A focus on active transportation and public transit is the way to go.