I understand your concerns but don't really think it's that big of a problem.
Messi has been rested in both games against Celta buy you can't really expect him to not play in every second game for a whole month. Anyway, how much did he really run (well, walk
) yesterday? There was a stat he had 4,6 km at around 60th minute so I guess he maybe made it to 6 km until the end of the game. He can't get tired because of that even if he's "playing".
Let's say this is our best XI that will play in CL (if everyone will be healthy).
MATS (0 minutes played in Copa)
Roberto (146)
Pique (283)
Umtiti (0)
Alba (180)
Busi (270)
Raki (159)
Iniesta (63)
Paulinho (125)
Messi (149)
Suarez (121)
Clearly, injuries have also played a part that Umtiti and Iniesta weren't used much in Copa (or not at all in Umtiti's case). But at the same time Umtiti and Masche's injury could also be a blessing in disguise as otherwise Vermaelen probably wouldn't get a chance to prove himself as another (at least) very important squad/rotational player which will be especially important now that Masche will leave and Mina will need some time to adapt.
Because of those injuries Pique has played much in CDR but I think he'll get more rest when Umtiti will be back (especially if Vermaelen will keep a good form and stay healthy) and Mina will get some minutes as well, probably from the bench in easier home games at first.
And Busi has played because we don't have a real replacement for him. But also keep in mind that he probably also wouldn't have started first game in Vigo if he wouldn't be suspended for the league match against Levante 3 days later.
I think Valverde has managed Raki, Messi and Suarez's minutes good so far in Copa. With Coutinho and Paco coming back from injuries soon and with our good lead in La Liga we can also afford to rest them (and possibly Busi as well) in easier home league games against Alaves, Getafe or Girona that are coming over the next month.
I'm not saying EV should go full Lucho mode and start 8 backups in those games (or even worse, in a tough away match, lol) and risk to drop points. But play 7-8 starters and 3-4 backups and you can give rest to anyone.
When Coutinho will be back and if he'll show a good integration with the team we can even play him as "10" and keep Messi on the bench. Or in another game, start a strong lineup, kill the game in 1st half (now that Suarez is back in form and will probably score more that should be easier) and then sub off Messi like we did against Celta.