Is the Philadelphia area the worst place to live in the United States if you don’t own a personal car ?

No, cities are typically better for people without a car.
Quite a few people rely on public transport and live in Philadelphia. 

The worst place to live (in my opinion) would be out in the country 100+ miles from town without a car or personal vehicle. Now don't get me wrong, I would love to be able to live out in the country if I could work entirely remote... but I sure would not want to do that without any form of personal transportation. 

Try Alaska.  My address used to be the mile I lived on.  78 hwy ***** was because I was the only person on mile 78 on that road... From the nearest city, and by city, town, and by town, I mean general store, with a gas pump.

Nope.  Try the eastern part of Oregon.  Or anywhere in Montana.

No. There are hundreds that would be worse, where the nearest grocery store, doctor, veterinarian, dentist, hardware store, drugstore, restaurant, and almost any other kind of store or service is more than 25 miles away and there is no bus and if there is it only goes once or twice a day, and while you may be able to call a taxi it will cost you an arm and a leg. The cab fare from my house to my nearest town is $90 one way. We don't have Uber or Lyft around here, and if we did it wouldn't be cheap either.

Any large city is easier to live in without a car than any rural area and many suburban ones. If you are in a large city you're likely to find everything you need within a ten-minute cab ride, if the bus doesn't go there.

No. Phoenix or Los Angeles would be the worst. Huge, sprawling metro areas with less than ideal public transit. You wouldn't want to walk very far on a 115° day in Phoenix.

I would think Los Angeles is the worst.  You cannot get anywhere without your own vehicle.