Cup competitions are usually for guys on the fringe, whatever the age. The fact that Van Gaal named Fletcher as vice captain clearly shows that values and appreciates what he brings, even if it's not as a starter. As for not needing him as back-up, I disagree. I would prefer Fletcher to Fellaini or Anderson, and really right now that's all we have. Of course, if we get Strootman or another high quality central midfielder then it's a different story, but I'll factor that in if it actually happens.
Fringe players to prepare them for the main team or keep them fit to contribute. Would make no sense to keep him to play cup games if we dont believe he can contribute to the 1st team anymore.
For the defensive mid position, we have Blind, Carrick and Fellaini. In case of emergencies, Jones as well. I'd play any of these 4 ahead of him. Signing Strootman or someone of his quality means little in terms of Fletch's role in the team because like it or not, he's just a backup squad player now, whether we get a top drawer CM or not wont justify keeping him as we have backups already.