Renting a home close enough to your workplace to make biking every day practical is usually more expensive than owning a car and living further away - especially if you have a family and need more than a studio apartment. In that sense, owning a bicycle and not a car is more expensive.
That said, this could be fixed with better public transit.
The average US commute distance is 20 miles one-way. That’s about 2 hours by bike at a slow-ish pace (10 mph). Did you accidentally calculate a walking pace (2 mph) which would take the 10 hours you suggested?
Before COVID, I used to often have a 45 minute commute by car or a 35 minute commute by bicycle. It's an 8 mile bike trip that is easy enough for me, a not particularly fit 56 year old, or a 9 mile car journey with 25 minutes of sitting in traffic. An electric bike would make it even easier to go further.
Who besides rich boys can afford to ride their bikes to work?
i bike to work in no small part because i can't afford to drive there
Single mothers getting their kids to elementary and middle schools?
in civilized countries, they can use a cargo bike (what the dutch call a bakfiets) to carry the kids. or the kids can ride their own bikes.
The elderly going to their doctors appointments?
many elderly people can still cycle. you may even see electric assist tricycles on the bike path in civilized countries. and of course elderly people also benefit from accessible and convenient public transit.
Working stiffs who can’t afford to live in downtown?
this is a real concern and i absolutely share your desire to build large-scale dense public housing developments in downtown around transit stations, as well as doing the same around more outlying transit stations such that taking public transit also becomes a viable option.
What do you think will happen to rents when is forced to get an apartment in one of the existing blocks?
wait, i thought you wanted to build public housing to address housing affordability? was that just me offering a solution, and not you? that's weird