Interactions, yes, but I wouldn't call those interactions socialising.
In my entire time as a child and teenager at multiple schools, I don't recall spending any time socialising with teachers and other faculty. Not once, and not even with my favourite teachers who made the most lasting impressions through their teaching, and willingness to teach me more advanced things than on the standard curriculum.
It was pretty minimal at university too. Socialising was with other students.
But the post by inglor_cz you replied to was specifically about socialising being limited to peer ages as a child, not social eduction in general.
Therefore your reply "this isn't really true though" and "how can you not categorise .. teachers" implied socialising with teachers and faculty, not just formal social interactions.
It really is true that many children don't have the opportunity to socialise with people outside a narrow age range at school, and that seems like a legitimate thing to dislike.
These are interactions, but form just a very limited subset of socializing. Most teachers remain fairly distant and unknown. Or at least that was my experience when going to school.
YMMV.
This is one thing home schooling has going for it, where the social life is built around activities with other home schooled kids who likely differ in age. It's much harder for kids to get caught up in the typical pet immaturities and stupidities of their age group.
Kids that have siblings, neighborhood friends, or social activities like boy scouts, which generally include children over a range of ages, really appreciate it.
It sounds like your school had access to this stuff already though, do you think it was valuable?