well yeah you could try it that way

In general I agree with Rob. You normally like players to make their knowledge checks. It does become a problem when you are following a character who is trying to hide and carrying a magic staff. He gets to roll stealth to hide from you, but you get to roll track to follow him and know where he is, perception for the same thing, and magic acuity to try to sense the staff. You could even try to roll perception again to try and get a feel of the crowd and their responses to see if someone just ran hastily into the market or whatever. There is a danger to allowing a person roll an unlimited number of times, restricting it only DM's don't want you to make the roll, and allowing all kinds of attempts when they do.

another example where maybe it makes sense though is say a prophetic scroll. The scroll is explained in an ancient language the character knows, but it's in a cipher. That language describes the whys of using a hermetic text at the end. In the whys section a few familiar religious figures and common motifs are used. The cipher used is a fairly easy to solve math problem and one that was used by known ancient religious sects. There are lots of way to solve this and it seems weird to restrict a character to only rolling 1 of the perhaps 4 or 5 skills they could use to unravel a mystery that is probably essential to the story. I think it's important that the DM not make the DC levels lower than they should be, but the DM should also allow that it's in fact reasonable, and more to the point how people actually solve puzzles, to allow the characters to try coming at the problem in different ways.

.......so uh that's all.