I'd say party-as-concept is inherent in the game, and always has been.
So then it would seem to be a combo of your decision and the way the game works, I’d think.
Well, it;'s either that or only one player gets to play what they want (i.e. their own character's arc) while the rest just tag along for the ride. Hardly satisfactory for the rest, even if the focus switches between characters now and then.
I mean it all depends on what it is the characters are after. There’s no reason that the time in the field can’t be related to a character’s goals. And no reason that can’t rotate with each mission/adventure.
The alternative seems to not allow any characters to significantly shape play, which seems limiting.
Also, are your players not fans of each others’ characters? I’d expect interest in the game beyond one’s own character. Otherwise, the character-neutral trips into the field would seem just as undesirable.
There’d also ideally be nothing that would prevent you from splitting the group up and handling them all separately. But this is another area where D&D doesn’t really shine, and so the way the game works influences the way it’s played.
If the players roll up a couple of Humans, a Dwarf, an Elf and a Hobbit for their starting characters I need to be able to pull out a map and show each player where - or at least what region or realm - their character is most likely from, based on its species and culture. Otherwise, I simply haven't done my job.
Alternatively, you can wait and see what the players want to play, and then determine what’s needed. If you wind up with two humans, a tiefling, and a dwarf, then you won’t have to do as much. Also, maybe there’s not a separate kingdom for each? Maybe the races are far more intermingled than a Tolkienesque setting? Or maybe things are even more different than that?
You can also solicit ideas from the players at this point. Maybe the player of the dwarf character has an idea about what dwarves are like in this world. Maybe he has ideas that immediately inspire some NPCs and possible conflicts.
Again… we’re talking about how much control is needed. The DM can loosen his grip in many ways, I’d say.