On the other hand, a bike-centric city would not be very accessible to people with disabilities. Having something in between, maybe trains or small electric buses, would be ideal IMO.
That really depends on the disability. If you use a mobility scooter for example, particularly one of the faster ones, that's going to drive much more smoothly on a bike path than on the sidewalk (where the pavement is often uneven, you have to deal with the curb every block, etc). For that matter, not everyone can drive either. Some disabilities result in your license being taken away; for example, you may not be able to drive if you're prone to seizures. But you may be able to cycle!
Now, you're right that people with some disabilities will not be able to cycle, or will not require a mobility scooter. (Although if you want one and can't afford it, that's also a problem, and I believe a common one here? Our healthcare system...) It's still important to have various accessible modes of transportation. Trains can be a good option here, though it's important that they have level boarding for wheelchair users and that all stations are likewise accessible. (Philly's unfortunately are not. The City Hall station reconstruction is long overdue.)
And some people may always still need a car due to their disability! In the Netherlands, they have something called the Canta, which is a microcar specifically for people with disabilities that's small enough to operate on bike paths and can be parked on the sidewalk: https://en.m.wikipedia.org/wiki/Canta_(vehicle)
And yes, some may need a full-sized vehicle as well; it's worth replacing some parking spaces with disabled parking spaces to accommodate that case.
My point, though, is that our car-centric city designs in the US don't accommodate everyone either! We often consider it to be the default out of inertia, but it's important to remember that not everyone can drive a car, and in a car-dependent area that's a recipe for social isolation. Our cities should be designed such that everyone is able to get around quickly and safely.
I can neither drive nor bike (safely enough) because my vision is too poor. I‘m happy to walk for a long time (anything under an hour), but any larger city should have trams imho.
However, bicyclists need to get their shit together in terms of pedestrian respect and traffic rules. I can cross a street pretty easily but crossing a busy bike path is a real challenge. I‘m sure we will figure it out in due time.
It also seems that the entire sidewalk is fair game for bicycle parking, which is a disaster for people navigating with a cane, but that can be solved with dedicated bicycle parking.
Context: I'm a cyclist that prefers no bike-specific infrastructure in downtown cores, but I think your pain is caused by (1) no dedicated bike facilities (lanes, parking, signaling, etc) and (2) inconsiderate or just ignorant cyclists. Turns out a bicycle doesn't magically transform the jerks nor the clueless into decent, aware people (I believe they do help though!)
I live in a city (Münster, Germany) that has extensive bike path infrastructure, but as far as I can tell, there is no established system for pedestrian crossings on bike paths other than "take care".
I would think that at a traffic light, bicycles should act the same as cars, but this just doesn‘t happen at all. I‘m lucky if bicyclists don‘t blast straight through a zebra crossing. It feels especially cruel for traffic lights that are placed between the bike path and street yet require a button press.
So it‘s two things: inconsiderate cyclists and and no common pedestrian crossing system on bike paths (or clarity on rules at existing street crossings).
That Canta car is pretty cool, I've never seen that before. Totally agree about car-centric problems. I grew up in the suburbs and lived near a lot of stroads. Requiring a car to do anything is such a stressful way to live.