I really don't think the crop "replaces" other aids. Gonzo cannot be ridden with a crop. Period. So if he's lazy, you have to use leg aids to wake him up, because if he even sees a crop, he's terrified. But, let's say he wasn't. . If I was asking him on constantly, and he was remaining at one speed. . then I might tap his shoulder with the crop as my next step, after he won't respond to my leg. But if he wouldn't go at all (let's say, trot to canter, or walk to trot. .) then I would use it on his butt. If he was just being annoying in general, I'd probably just carry it.
With Roger, I carry one because it reminds him not to be naughty. I'm not saying I want him to be afraid of it, but he's still rusty at cantering, and when I have it, his transitions are a lot better. I try not to rely on it, and I do canter him without it as well, but yeh, sometimes I like to have it just so it's easier on me. Two other things I use it for with him? 1) I bring it while we're walking down to the ring. If I'm not on him, he will not move at all, and he's a real a*s on the ground. . ;) So if he acts up, or refuses to move, I'll tap his butt. 2) He will try to get me off now & again. So, if he's being really, really bad, I might smack him (not extremely hard, but enough to get his attention) to tell him he's bad.
With Rupert, I just like to have it because, he kind of runs into the canter. So I use the crop to wake him up and he's like, "oh. . we're cantering." and then he goes. hehe. Milo is extremely spacey, so I use it to remind him to pay attention to me sometimes.
Dunno if that helps, sorry for the novel, hehe. . but yeah, I think they should be able to if they know how to use it right.