https://www.bikeleague.org/content/national-household-travel...
The vast majority of people making those trips are able-bodied people in urbanized areas (80% of the US lived in an urbanized area as of 2010).
https://www.icip.iastate.edu/tables/population/urban-pct-sta...
So if you can get bike infrastructure to where people are living, you've attacked a big chunk of the auto problem.
Per your second point, yes, it can be feasible. The modern rural US is very sprawling in terms of the built environment but it wasn't always that way. Rural areas in the US used to revolve around small villages and points of density that service a wide area, complete with transit connections. Many German rural villages are extremely bikeable and have regular transit through their regions and to larger cities.
You still can accommodate people who need vehicles, just the demand on infrastructure (parking, number of lane miles, subsidies and costs) would be greatly reduced. As it is now, the children, the disabled, and frequently the poor can't drive themselves and rely on other people driving them. Cycling can be done by almost anyone, is much cheaper and therefore much more accessible than driving.
But I don't think bicycles and mass transit will take over ultimately. But self driving electric vehicles a bit larger than a bicycle could do it.
These will only need one seat and minimal storage. They'll go directly from home to work without stopping at every bus stop or train station along the way. And they'll be 1/4 the cost of today's car.
And, yes, they won't work for everybody and every situation, just like everything else.
https://www.un.org/development/desa/en/news/population/2018-...