Actually apartment buildings are mostly concrete. Strip away finishings like cabinets, drywall and flooring from a unit, and what's left is a concrete cell. Sometimes separating walls within a unit are wood based but that's rare too.
It’s called a 5-over-1 and it’s so much cheaper than doing five stories of metal pan and concrete deck that the economics force the decision. You see these everywhere.
https://en.wikipedia.org/wiki/5-over-1
Anything over 6 stories will be concrete and steel, or rarely, engineered wood or timber framed.
Concrete and steel apartment buildings do not have vertical concrete partitions or wood stud walls between the units, they have steel stud walls with two layers of double 5/8” drywall on each side to provide a 4-hour fire rating.
I am a construction professional, FWIW.
I've lived in pretty large buildings (eg dozens of units and four floors high) that were largely made of wood in both the northeast of the US and California.
They aren't high-rise buildings but I wouldn't argue they aren't apartment buildings, and they're far from uncommon.