As someone who loves trains and buses and planes, I wish that people who pushed public transport would actually engage with the reasons why people don't want to use it rather than just making alternatives worse.
There are three main issues that need to be solved for even me, a train lover, to prioritise using them.
1) Undesirables need to be removed. I don't want to deal with beggars or other general hoodlums. Transport police need to be aggressive with stamping out these behaviours. If I have to interact with these people I won't do it.
2) It needs to be clean and comfortable. My car has air conditioning. If I have to feel sweaty and worry about touching surfaces I'm just not going to do it.
3) I like a good walk, and there are also real limitations to scaling here, so I'm less rigid on this, but it does need to go roughly to where I want to go and it needs to be frequent. If I'm out in the rain for fifteen minutes waiting for a bus I'm just not going to do it, I could already be halfway there by car.
I don't think these are insurmountable, Japan does pretty well, but in the absence of that, the stick just isn't going to work. If travel times via car doubled, I'd probably just do less and then eventually move out of the city.
edit: I can't reply about libraries due to rate limiting.
Libraries are a great example of how public transport _could_ work!
I love libraries!
The British Library is truly public. Anyone can go, anyone can enter the reading rooms. It is a lovely environment to read or work in, as they have strict rules. It is peaceful and pleasant because of the way that it's set up.
It's also a great example of how the many can come together to do more than the few. Almost no-one is able to create a home environment with that sort of atmosphere, and by sharing it we all get more.
I would love it if public transport were like the experience of using a good library.