I don't think behaving more like kids is something confined to dads, or even men as a whole either. It seems modern adults are maturing far more slowly or even showing some signs of regression now.
I don't have anything to compare it with, but grown men burning their evenings in front of a games console, playing games aimed at children, and grown women slathering pictures of themselves all over social media in an attempt to garner attention and social acceptance, with both groups seeming to want to be their kids' "buddies" more than ever, doesn't seem to be a positive direction for things to go in.
Who knows. I may be bah humbugging here. I'm young enough that I can't reasonably say "in my day adults were adults!", just that the direction things appear to be going in (socially, and as role models for children) does not appear to be promising.