Personally, I think this idea wouldn't really change how people play the game.

What it would change is that it would reduce how punishing some jobs are in regards to drift. If you allow, say, Gluttony on RPR to cooldown overflow for half its CD, you reduce how punishing it is to drift it because it will always be up unless you somehow pressed it 1 and a half minutes after you were supposed to. Same goes for other jobs prone to drift like MCH and GNB.

While it would certainly make some jobs less punishing to learn, I don't personally see how it could increase the skill ceiling.

But if your main aim is to make jobs less punishing while also increasing the skill ceiling, I'd say make 60s buttons into 40s buttons. If someone doesn't drift, they get one extra cast in between burst windows, but if they're prone to drifting, they still get it for burst windows (assuming again that they don't play really badly).