Here’s a better theory: because American public transit is, when compared with the alternatives, not safe, not clean, and not convenient. Take LA, probably the most car-dependent big city in America. Riding the bus or subway in LA is not an enjoyable experience. Nor is it enjoyable to walk around the areas where the stops are. If I were trying to get more people to use public transit, I’d start by making the stations and buses/subways beautiful, clean, safe places that are just nice urban places to hang out in. There’s no need to make it a moral crusade; just offer a better product and more people will use it.
*I say "perceived safety," because vibes seem to matter more than actual safety. Like, the stats on car wrecks, drunk driving, distracted driving, and so on are alarming. But when I think of someone concerned about "safety," I imagine someone being uncomfortable around people they feel are sketchy.
I think an interesting thing to remember about perceived safety, statistical safety, and actual safety, is that they are all different things -- you can't just look at stats to determine actual safety.
E.g., I was involved in a couple of incidents involving attacks in SF that I am sure were not reflected in the stats. (As well as numerous thefts, though that's not a safety issue per se.)