You say "it's impossible because X", but what is usually the issue is that cars just take over all the space and make public transport, walking and cycling impossible. I could live in the country side without a car thanks to the pandemic, I do understand that most people make choices in their life that make that harder, but those are choices made by people and infrastructure planners. They are not fixed truths.
There is so much to disect here and I do not think we can reach a common conclusion because everything is a special case. For reference I lived 9 km to the primary school, bus and store, 60 km to the nearest hospital and train station, 4 km to the nearest daily bus. I understand that it might feel strange to build bicycle infrastructure in such an environment. Luckily for us it was perfectly possible to live there and have my children ride their bicycles to school, but this was only possible because a lot of people alreadt walked on these roads, and it was quickly known in the community that my children rode there in the mornings, even if they were the only ones doing it.
Yes you need to change the infrastructure even in the country side to enable walking and cyclists, it does NOT have to be 10km of cycle track, but it might have to be that.