But top 5 universities are just 5 universities.
Now mine went to a 10K school so not huge- and had tight relations with several. I know a Purdue mom has said on here her kid has/had strong relations with profs. In her case though, she was in two cohorts within Honors - so very small groups - perhaps to repicate an LAC. I had one at Syracuse (not mega big) where I had strong relations. Had Thanksgiving at my Spanish teachers house freshman year.
It may not be as often - and the kids may not seek it out - but one can certainly have close relations with professors with large classes.
But the percentage of kids who seek that out is likely far, far less than at a small school.