We got a switch when it first came out, that was the only switch we had as a family for a while. It was shared just like any other console. Games like Mario Kart are just as playable on one switch as they are on prior platforms, if you buy more controllers.

Eventually, as the kids got older, we got them switch lites so they could play games on their own. Physical cartridges are definitely sharable, the only catch is that (of course) you can only play one copy at a time and some games have an online/group play component that you can't experience with one cartridge. So, for instance, Animal Crossing has one island per switch, so if you have two switches in the household you could swap the cart back and forth and both switches can play the game by swapping the cartridge, but characters from one can't visit the other unless both games are running at the same time. We have bought an embarrassing number of Animal Crossing carts.

Digital copies are tied to a Nintendo account. You can only have one "primary" switch attached to the account. That Switch will be able to run the games on the account without phoning home first. If that account is logged into other switches, they do get access to the games, but only if the non-primary switch has internet access to validate that the game is not being played by any other switch on the account. (I ran into this issue whe I wanted to play the BOTW DLC on a second switch on airplanes; I ultimately had to create a second account to buy it a second time on that switch to prevent it from phoning home).

Digital copies also download the entire game into storage, while physical copies have the game in cartridge ROM and much less is stored locally. Getting a Digital copy of a large game might fill up most of your storage. This is why I still prefer cartridges, especially now that my kids are older and don't lose them anymore.

How is it affordable? It's not, we eat a lot of ramen.

Hope this helps!