Slice isn't an abbreviated groundstroke and players who hit the slice properly use both a takeback and a follow through coming up to the shoulder just like a groundstroke. You CAN get away with not doing that on the slice but you could also get away likewise on a groundstroke. It's just that modern coaching emphasises groundies way more than the slice so it feels like one can get away with subpar technique on a slice.
Also, the overhead is all or nothing. If you hit, you're more likely than not going to win the point. If you miss, you lose. The slice is primarily a defensive shot though the best slicers can turn it into an attacking weapon. You're only looking to neutralize the incoming ball, not to whack a winner. So the margins also favour you on the slice compared to an overhead.
If you grew up playing a sport like basketball, you will probably find the overhead very intuitive. But if you can't judge the trajectory of a high ball about to drop on your head, the overhead is very difficult to time. There is no such issue on the slice. As to your point on the speed of the incoming ball, that applies to any groundstroke and not just the slice. Likewise, a deep lob would require much more footwork and judgment to hit a good overhead off. You may even have to jump-smash a la Sampras. Those aren't easy things to execute either, especially in tournament pressure. But if you're even reasonably good at the slice, you are not going to miss it in the clutch.
Just think of this. You see even the best players at the pro level, the greatest in the world, players with good overheads, make a mess of them once in a while. But you never see them similarly botch a slice. The height and depth of the lob always adds an element of unpredictability to the overhead. It's the only shot where you hit down on the ball (even in a serve, you're reaching up and extending to the ball and have more control over it being that you're tossing the ball). Every other tennis shot is down to up and hit off balls getting no higher than your shoulder. I mean, unless one purposely wants to hit a groundie off a ball that's up to his head for some reason.