First and simplest usage case is hitting startup or ending lag. For example, a lot of Marth's moves have a fair amount of ending lag, so you can threaten running shine a lot more than in most matchups. However the principle is applicable to many other matchups. Another example: if you can get in uncomfortably close to opposing spacies, the running shine may be able to hit them out of any jumping option before they get an aerial or laser. However you need a head of steam going into this to make it work.
The second case is a bit more complicated and basically can be used as a low risk high reward way of crushing someone's footsies game. Ideally you'd hit a dash dancer on the back part of their DD. However in practice there are times you'll aim elsewhere. If you miss in any case, you can wavedash out and minimize your commitment. if you hit, you can get a nice punish off of it.
You're right on the crouching point. There's a somewhat larger minimum space requirement to pull off, but the second case I mentioned uses more space to call out their DD, so that's why it's a useful tool there.
It's useful to some degree in most matchups, so theory and experiment with it. Just be careful if your opponent is zoning well.