I've never run into a walkable city center where there was one super-obvious and convenient place to park--maybe a gigantic underground garage--and then you walk everywhere from there. Feels like that might work.
The attractive city centers have nice stuff, but too few people who live within walking distance to keep them in business and in good shape. They need a way to bring in suburbanites and visitors to supplement the native population.
In a lot of areas, street parking is actually a really good way to provide a barrier between the sidewalk and traffic. This physical safety provides psychological safety, so people feel a lot more comfortable with sidewalk dining, etc. A lane of parking can also separate car traffic from a bi-directional pair of bike lanes.
Also, a lot of cities have too many and/or too wide lanes, which makes drivers feel too safe driving unsafe speeds. You can use parking to "eat up" the extra space and make the street feel more crowded, which will make drivers slow down and drive a lot more carefully.
So street parking should absolutely not be seen as just a negative thing, it can serve a very useful function in the layout of a street.
On a similar note, my city used to have a lot of 50 km/h four lane streets through residential areas, even though they were only minor trunk roads that didn't warrant that many car lanes. There was also a severe dearth of bike lanes, and since these are residential areas with lots of houses, there were always cars parked in the right lane and cars turning left into driveways.
The solution was to remove two lanes of traffic, forbid street parking, add a bike lane along each side of the road, and add a centre turning lane. this was all done with just paint and "no parking" signage. There was a bit of complaining about the loss of street parking, but other than that it's worked out great, and I actually see people using the bike lanes now, and traffic actually flow smoother.
Montreal is similar. Parking downtown: horrible. Parking out in the 'burbs and then riding the metro into town? easy, and lovely. For a lot of things, anyway.
Might be a Canadian thing. Toronto is similar. If I recall correctly, Toronto operates the second most used public transit system in the United States or Canada, while the public transit authority there is the largest parking garage operator in North America.
It’s a pretty good solution for medium-sized cities, but it breaks down as population increases. Toronto has largely stopped building these garages because they’ve run out of room for them after immense population and ridership growth.
Toronto is a pretty big though, so it’s still a solution worth exploring for medium-sized cities that can still reasonably build these facilities.
In Europe this is solved by having a train station in the center. Even the little towns have them which is why it can be lovely to spend a day exploring the area whereas in the United States it’s often easier to assume a small town will have little walkability and maybe you’ll just stop there for gas.
The attractive city centers have nice stuff, but too few people who live within walking distance to keep them in business and in good shape. They need a way to bring in suburbanites and visitors to supplement the native population.