Imo, street side parking in cities should just be scrapped. It makes no sense for the public to pay so much money to allow people to park particular kinds of private property for free. Pushing all parking on to businesses own lots or in dedicated parking facilities would let the market adequately price parking rather than externalising the cost.
In my building, there are 40 units... and 6 parking places in the basement. Most of the city is this way. Street side parking is the only way to go. TBH I prefer trees and grass over parking lots. I would not change it.
I don't see a meaningful distinction between a consolidated parking lot and one that's distributed along the side of the road when it comes to tree and grass cover. For dense urban situations car parking buildings allow more than either surface lots or surface street parking.