Nitter's a great site but I use archive links for OPs since their longevity is a lot more reliable than say, something that just mirrors everything posted to twitter. Say I saw this right after it was posted to twitter. Regardless of its initial shape, anyone coming to it now would see the tweet at issue is now unavailable, making the entire post pointless. If I happened to make an archive link right when I saw that tweet we'd still be able to see it in the archive. We've lost god knows how much info thanks to tweets or what have you getting deleted and no one having the foresight to archive them.

There's also the benefit of people seeing the archive more easily and being able to get to its content more reliably in the future. I could post one in the comments but as often as not those just get buried and the chance of anyone seeing those decreases with the post's age and comments.

Of course, archive links are useful if you want to avoid giving a site clicks, but I would say my purpose in using them as OPs is as much archival as it is letting people know about something interesting.

edit: I was needlessly flippant in my original reply. It would be great if there was a good way to archive embedded videos because telling someone just go to the original isn't much help later on down the line.