In my experience it's mostly due to convenience. When public transportation is available and more convenient, it's heavily used. It needs to be available everywhere and all/most of the time. Car pooling is similar, coordinating with other people, leaving home/work at the same time everyday is difficult, not convenient. If Lyft is widely used, it can solve this problem. No need to have advanced plans. In fact, in Washington DC, I can see people offering these rides for free to a second person in the car and use the HOV lanes. This is already done from fixed locations without the help of an app. Lyft would make it so much easier.

If people aren't willing to a share car with a stranger for money then Uber wouldn't work. It really is that simple. The evidence suggests that they are. The 'will people share someone's private car?' question has been answered and it's an emphatic "yes". That isn't the whole story here though.

There is a possibility that people wouldn't want to give up the convenience of commuting - having your car at the office so you can go somewhere on your lunch break, leaving the office without having to wait for your carpool ride, carrying large items to the office, and so on - are benefits that you would lose by switching to Lyft. People will have to weigh those benefits against the cost and stress of driving to work. So the question here is really "Do enough people want to give up driving themselves in favour of a cheaper, easier, but mildy inconvenient alternative in the form of Lyft?". The answer to that question is not an obvious "no". There could well be a big enough market to sustain a profitable business.

The fact that people haven't carpooled much before is not evidence that they don't want to or that they can't be persuaded to now; it is simply evidence that the pain of commuting was lower than the pain of organising a carpool. If you can lower the effort people have to put in enough so that it's sufficiently easy to carpool then it is possible change people's minds. Lyft will succeed if they can do that.

It's entirely possible that I'm being biased as an American, but I've never really felt this way. I love public transportation whenever I'm in cities like Chicago or New York City. My issue is that my state (and sometimes my commute) is bigger than most European countries. I've never felt a deep cultural barrier between public transportation and me, it's personally just incredibly inconvenient. I would very much love to see more public transportation options in America, though. But your argument is quite interesting, so thanks!