I see where you're coming from OP, but I personally don't think it would work for a couple of reasons. The first is because that mechanic would draw potentially too much attention to the party system as a whole. People already have issues with not being able to take their whole party out with them in games like this, but I suspect that most players shrug it off simply because the headcount limit a common convention of the genre. Gamefying it in the way you describe without a good justification could draw more explicit attention to how arbitrary it is, which could rub more players the wrong way.
The larger problem I see though, is that that severely party interaction. Only being able to have two or three characters in your party means that you potentially miss out on character stuff like what GM pointed out. And I'm certain a lot of players play games like this for the character interaction and character story, so forcing them to miss out for a long stretch of time would be pretty disappointing. Furthermore, I think the experience you describe of reaching level 3 with a full party in 15 minutes won't be the typical experience. I typically don't hit level 4 until several several hours in. I usually am at level 4 a bit before I'm ready to go to the goblin camp, which I think is the intended progression. You are right though that you gain levels faster in the early game and it slows down by around 5th level. From what I understand that's how the D&D system is meant to operate.
