Removing parking spaces puts more cars on the road -- circling for spots and parking illegally in traffic lanes.
If you want faster buses, evict the cars from the bus travel lanes.
If you want faster buses, evict the cars from the bus travel lanes.
Same with parking. You build parking in areas where you anticipate increased demand or already have unmet demand. By building parking, you increase your capacity to meet that demand.
If you have unmet demand (i.e. not enough spaces for the volume of vehicles that wish to park in an area), you're limiting the economic throughput of that area. Yes, you're reducing traffic congestion in the process, but at a very real economic cost for those whom were being patronized by that now-gone traffic.
Same with anticipating new demand. If you're building in an area, you want to be sure the area has enough parking capacity to absorb the intended volume of people traffic your building will have. If you're building a new skyscraper or mall or big box store, that's likely not true. So you incorporate parking into your project. Once your building (and parking) come online, you'll start attracting a higher volume of individuals to an area. Which, except for the most underutilized or mature transportation networks, will have a corresponding impact on congestion due to the greater throughput of individuals to the area.
If you have mature public transportation, then your transportation network likely has the bandwidth to absorb this throughput increase with a lesser impact on congestion than if you're in an area with immature public transportation options. But mature public transportation tends to be very expensive to build and maintain. Which is only likely to happen after growing to the point of having heavy enough congestion to make such expensive and regionally disruptive changes both politically palatable and economically feasible.
I do not envy urban and transportation planners.
That's hard to do without BRT - we have plenty of dedicated bus lanes (the right lane) around here, but they all allow cars for right-hand turns, so buses still get stuck behind a line of cars.
Without BRT and center-island boarding, it's harder to reserve anything but the far-right lane since the bus needs to get there to pickup/dropoff passengers.
Dedicated bus signalization, no right turn on red, and cars perform right turns from the second lane. Dedicated signal phase can be combined with separated bike lanes to improve safety for other road users, as well.