(Edit: not that these necessarily need car parks, but they'll need to wait somewhere when they're not carrying passengers)
This claim has been made for years now and a number of big companies like Google, Uber and Tesla have tried to jump into this market, but does this hold up?
I vaguely recall a self driving taxi service being active in some areas, but how are they doing?
Anyway, static routes and stations work fine for big parts of e.g. the Netherlands, but you need a good structure of bus routes and transit hubs. It's a fact that it takes longer than driving for most trips though and IMO the cost should be a lot lower, but that's the tradeoff made.
It's not even remotely competitive, and for that reason private cars are used for some ridiculously high proportion of journeys (90% of passenger miles overall).
In the UK only 17% of commuters use public transport, and 5% use "other" including bicycle/motorcycle/taxi.
I think a lot of what you're saying can be solved with cheaper ebikes and better bike infrastructure. Even the rain :-)
If it rains a lot you put on a big bike poncho, which turns you into a big sail and slows you down, and that's where the <<e>>bike part of ebike comes in, since you pump up the assist and still go fast.
The consensus seems to be on my side in spite of lower share of total commutes, because housing near stations is significantly more expensive. From that I infer two things, public transport is desired, and there's not enough of it to support demand.
This is only because of the suburban sprawl we built not being compatible, but I agree it is a problem to solve one way or another.