And I get those arguments. I think TES could have better class systems.
But I don't think Skyrim's classless situation makes things any better at all.
Here's the problem with Skyrim: The game immediately kills any sense of roleplaying and immersion for me because your character has no history. Every single person of a given race to cross into Skyrim is, apparently, equally skilled at lock picking, fighting with massive war hammers, conjuring ghosts and shooting bows - as well as everything else. This completely ruins the game for me. You cannot play a Khajit thief who's fleeing into Skyrim or an Imperial knight-errant trying to cross over to investigate the civil war because the game refuses to allow you to have any skills that you might have developed beforehand. Everyone's walking into Skyrim as a fresh slate, some empty canvas that apparently wasn't born and raised, but rather simply popped into existence as a fully-formed advlt just outside of Skyrim - and while that may be funny and a little creepy on a meta level (because technically it is what you are), it's horrible for role-playing and immersion.
So, sure, we don't want to have classes. That's fine. Why not integrate something else then? Fallout's "tagging" system would work wonders for allowing us to determine skills that our character might have cultivated prior to the start of the game, or is naturally gifted at, without forcing people into the confines of a class. You could even bring back Major and Minor skills. Heck, even Primary skills, if you want to go back that far. You could tag one skill as a Primary skill (+15 bonus), three as a Major skill (+10 bonus) and five as a Minor skill (+5 bonus). Or not, and just have three skills you can tag like in Fallout. Maybe even have the tagged skills increase faster.
This allows you to form your character into something real and actual.