I've got a few like that. The reel can be so out of whack that it'll damage the tape eventually (so you won't get a decent wrap and eventually the tape will curl). I replace the reel but store the original with the box.
I also have some records that I do a similar thing. Sometimes the inner sleeve is really cool looking but since it's old, it sheds lint like crazy. I get a nice new inner sleeve and save the original so I can look at it.