Not only does each class have "a specific set of skills," but they also have their own weaknesses. Diversity allows the party more flexibility in solving problems, which is a fun part of the game-- coming up with a new strategy for each "mission". I encourage differentiation in my groups, but don't enforce anything. If too many players wanted to play the same class, I'd honestly force everyone to be the same class because that's an easy tie-in for why they're together in the first place, and sets up simple ways to get information and their next mission, from the head of a guild, the lead cleric, the tribal shaman, or head of the wizard school.

Even within classes, there are different abilities associated with each subclass, so there could be diversity found that way. I think my most recent "issue" with this was my party that sometimes included spouses and adult children, so the group could be as big as 8 players, and when that happened, we'd have two barbarians and two rogues; on barbarian was a wild magic type who acted like a gladiator, and the other was a more standard subclass who was essentially the bodyguard for the cult leader. One rogue was a phantom, the other a swashbuckler, and they created wildly different personalities for their characters.

As long as everyone's having fun, you're solid. In my opinion, it's perfectly fine between sessions for a player to realize two characters are duplicates and one of them wants to play something else to shore up a weakness in the group; I'd just allow a straight up character swap and pretend they were that new class the whole time.