The purpose of academic visits seems obvious: research flourishes during close interaction with colleagues in a scholarly atmosphere.
If you can’t get a grant for an academic visit, try the “Share Screen” function on Skype. It’s like arguing in front of a whiteboard or hunching over a piece of paper, but if you get tired, you can just put the phone down (and blame the connection).
So the real reason for academic visits should be relaxing dinners with your co-author.