Not sure about Spain, but in Italy, you definitely find a lot of 'family size' flats. We had a 3-bedroom, 2-bathroom flat in a 6-plex, and that is a pretty common sort of living arrangement.
What's the area of those flats? Where I live there are plenty of 3 bedroom flats, but they are usually under 100 m^2 (often smaller) and almost always under 150 m^2.
I live in Spain in a 85m2 [1] and it isn't cramped in term of room sizes. In fact my 2 daughters decided to live in the same bedroom which meant I could convert one to an office since I am working remotely. Having said that 100m2 would give us access to a second bathroom which would be nice considering there are 3 girls living in the same place. 150m2 would be overkill for 3 bedrooms, I guess it would be more a space for 4 bedrooms or 3 bedroom and a dedicated office.
[1] caveat is it is not an appartment but a townhouse with a commercial space in the main floor. It give me exclusive use to another 85m2 rooftop space with a washing machine there so I don't have to dry clothes in the living room + exclusive use of the stairway where I store our 8 bicycles and the standup paddle. But I would say that if I didn't have those extra space I would just not have so many bicycles and things and would hang the clothes to dry hanging at the windows like everybody does.
There's plenty of 150/200/250 m^2 flats in Italy (Rome and Milan especially), but they are very expensive.
Here's a non comprehensive list of actual apartments above 250m (I didn't filter by flat, but you can see plenty are) and this is only the core center of Rome (what would you call downtown), not the entire city.
Is 100m^2 really considered cramp for a 3 bedroom? Admittedly I'm from the uk which is famed for our small home sizes. But I've been looking at 2 or 3 beds recently and anything over 80m^2 felt huge.
100 sq meters is about 1000 sq ft, and that's definitely on the small side for a 3 bedroom. 150 at 1600 is much more "normal" even in the US (for apartments, houses are usually bigger now).