I grew up in a small house, and Zillow thinks it was 672 square feet. As it's a rural home, I'm going to guesstimate that they are looking at the footprint only, and it is actually 2x that size.
So, 3BR, 1 BA, 1300 sf.
I'm the 8th of 9 children. We are pretty well spread out. I'd say that max # of people in the house was 8, but most of my life growing up, I'd say we had 5-6. One of my older sisters moved out when I was around 12, and my brother was 10-11, and one other sis was 18. Before age 12: 6. After age 12: 5.
I mean, it was fine. My brother mostly had his own room after the age of 7 or so. I shared the "big" bedroom with two sisters. I don't remember it being any issue at all, really. My sisters shared a double bed!
I don't see this attachment to having your own room. I had a friend tell me once that I'd have to upgrade my 2BR house to a 3BR even if I had a second boy because they need their own room?
I got my own bedroom when I was 22. (Rented a room in a house.) For the rest of my life, I shared. Oh, except for a year or two in HS when my parents divorced.
You don't need to give each kid their own room. However, if it is laid out correctly, you can get private time.
4 people in a 2BR, 1BA, 1100 sf house can be hard for private time...but honestly, 2 bedrooms, a front porch, a back yard, a bathroom, and a living room. Everyone can get away somewhere. Even all at the same time.
Also it depends on where you live. I live in CA. I grew up in PA, so yeah, we lived in a tiny house where it got cold in the winter. We went outside anyway. My relatives back there have larger homes - if you've got active kids, it can be helpful to have a basement in the winter so you can kick them down there to play.