I don't like them when it's a retired player. Especially long retired.
I don't generally like cutting up anything, but I can see a few things that I'd make an exception for. Like if the jersey was too far gone for much else. Or the bat was a partial bat, like the ones I saw years ago where someone had an in with a team to get broken bats, sliced them in half the long way and added pegs to make bat hangers and coat hooks. Basically if it's already wrecked.
(current players, no problem. They can literally use a bat for one pitch, send it back to the dugout for another and it's game used)
Here's an item that would be borderline. A braves warmup jacket, bought from a local auction. I never looked at it in preview, it was just hanging up behind one of the tables like it was someones jacket. Announced as Ernie Lombardis and coming from a family that was friends with him. I can't even find pics of the warmup jackets to know it's a real team used one, but it's very well made, and reversible the white side is leather, and pretty torn up in the shoulder area where a name would have been.
It went cheap even if it's from one of the bench guys, and if it's not game used I could fix it and wear it.
Would it be a huge loss if a card company cut it up? Maybe not, even though I cant find anything similar. Is it really cool as-is yeah, I'd rather have the whole thing.
I don't really go out of my way to get those cards, but if I end up with one it's in the collection.