The answer to this is, I think, “no one really knows.” When we discuss balance, especially when we discuss broad, systemic things like this, the approach to answering these questions is to leverage the expertise of a wide consensus of players, who have tried tons and tons of things and have come up with either “haven’t found anything broken yet” or “yup, XYZ totally breaks things.”
The problem here is that this is not a widely-used or widely-considered houserule. Paizo certainly doesn’t keep it in consideration when they design things, and you’ll find few—if any—discussions online of play under such a houserule. Without a big, broad base of testing and experiences, we simply can’t know the answer. Even if I had played in such a game—and I have not—it wouldn’t necessarily prove anything. If nothing was broken, is it because the houserule is fine—or because we just got lucky and missed the problems? If something was broken, does that mean the rule is unsalvageable—or does it mean that one thing needs to be addressed because it breaks, but generally the rule is OK? We just don’t know.
So if you are considering such a campaign, know that it’s necessarily going to be experimental. If you are the GM, you are going to have to do more work considering and vetting player characters than you otherwise would. If you are a player, you are going to have to expect more ad hoc rulings from the GM, possibly even including a ret-con to your character to eliminate a combination that proves broken. I have played in and run plenty of experimental games, and for me, at least, that’s fine. I haven’t tried this particular thing but if I had players who wanted to, or if a GM I knew and trusted was suggesting it, I’d be fine with giving it a shot. It might well be broken, but maybe only a few specific combinations are that we can ban or houserule or just come to a gentlefolk’s agreement about, and play can proceed. I am comfortable and confident enough in my judgment and the judgment of GMs I play under to do that.
But it can be a tall order for a GM who has less system mastery, or for players who find it a struggle to create and recreate characters under shifting rules and expectations. I definitely wouldn’t suggest it to a new GM or for a game with new players.