I think recutting anime OPs can be a lot of fun, and can be excellent editing practice. Whether it's just because two songs sound similar, or because you have a joke you want to make, there's some good content potential out there for it.

I, personally, have done it a few times, but only ever kept the two Berserk ones I did:

Anime: Berserk (1997)
Audio: "Boss of Me" - They Might Be Giants (Malcolm in the Middle Theme)

Anime: Berserk (2016)
Audio: "Tell Me Why" - Penpals (Berserk 1997 Theme)

I was thinking that we could start doing some of these and post them here!
If we do, though, it may be good to mention the anime name and the audio source for anyone wondering.