Echoing that I really don’t think that most Americans share bedrooms unless they are really really poor, and then they’re most likely sharing with extended family. “Roommates” to most people just means sharing an apartment/house.
Even most colleges don’t require students to live on campus, so living in dorms (ie, sharing bedrooms with a stranger) is only a single year, or even a single-term proposition until you make friends and work out a better housing arrangement.
Once a student makes friends or joins greek society, then there’s a built-in pool of friends and acquaintances and housing options - all you need is two-to four people to make it affordable, and lots of people rent specifically to students.
There’s no huge barrier to entry for renting - if a pair or a quartet of friends pool resources, that’s usually enough to pay the safety deposit and the extra-month(s) rent, and then to keep up with utilities and rent ongoing. You make it sound so complicated and stringent with talking about applications and comparing housing to finding a job. It’s not like that at all for most people.
Now, sure, people do advertise for roommates all the time, and yes, you’d have to go and meet them and see if you all can basically get along, but it’s still not nearly as formal and difficult as you make it sound. Either you mesh (or are indifferent) or you don’t.
I technically lived on campus all four years (it was required for the first three, and strongly advised for the last) and shared a bedroom with my previously-established best friend for the first two years. The college encouraged friends to note who they wanted to room with.
Junior year we had more like a townhouse or a condo - a quartet of bedrooms with a shared kitchen and living room. The school encouraged students to register for housing with friends or fellow study majors, or shared greek affiliations, so all four of us were friends.
Most of my senior year I spent housesitting for a wealthy friend, and our quartet (sometimes six of us) mostly lived in that house instead of our dorm rooms. We were a pair or a trio of couples, and we lived together like a family, with bedrooms divvied up, but sharing the living quarters and just hanging out.
Later, we moved on to an actual rented house, and there were up to eight of us (and all our cats…) living together for a few years. All of us were friends or lovers, and we managed quite well. Several of us actually did poorly once we had to move away (for jobs or into actual married life) because we were lonely living by ourselves, or just as a couple.
I don’t think it’s strange at all - you just get used to the fact that “your” area is just your bedroom, and the shared areas are general social spaces. I can see that it would be weird living with someone you didn’t already know well, but as long as people are polite (and you have a lock on your bedroom door) it works fine.