Well the point is that you'd have to start the edition and place the classes in the groups you design them around.I understand conceptually what you are going for... but when you use the example of Warriors getting Extra Attack but you then have to add Rangers to the Warrior group temporarily in order to give them Extra Attack too (and presumably add Paladins too)... I just can't help think it's just as easy to just list the classes that get Extra Attack rather than create a "group" and then have to include a whole bunch of exceptions in addition to it. What exactly is that Group designation saving us? And Arcane magic? Well, you either strip the Bard of Arcane magic and turn it into something else, or else you have to keep saying "the Arcane Group AND Bard", which is just as many words as listing "Wizard, Warlock, Sorcerer and Bard", so again, what's the benefit?
And while 3PP could create content with Groups in mind... they could just as easily create content that lists specific classes too. I mean look at all the exceptions would would need to make-- magical plate mail? Can't say "For the Warrior group" because Monks and Barbarians ain't going to use it and Paladins would... which means you end up just having to list the classes anyway. And there will be plenty of time you'd want to give things to all the nature classes-- Rangers, Barbarians, and Druids-- which would preclude any Group and you'd end up just listing classes again.
Now that being said... yes I agree with you that a whole new edition would in fact be the best time and place to work on it because you could strip everything back down the foundations and try to build them back up so that Groups could be a thing. I just don't know why it would be all that useful even if you could. But I won't dismiss the premise out of hand... maybe when WotC decides to make 6E whenever that is, they'd be able to convince me otherwise? I will fully accept the possibility.
Then design exceptions when they see fit.
I think
Orichalcum Armor, rare (requires attunement by a Warrior class)
is better than
Orichalcum Armor, rare (requires attunement by a barbarian, fighter, monk, paladin, or ranger)
and the DM is allowing Warlords and Bloodhunters