Until he makes it through a full season somewhat healthy, the rest days are going to stick around. I agree that it is unfortunate. But he has more value 4 days a week than he does 0 days a week.
I am willing to bet he is the DH more than 40 times this upcoming season. He would have been last season, if he had not sat out or if Gary Sanchez did not go on the hot streak he did. Also, would be surprised if anyone on the team goes much above 50 games at DH (unless they sign a full-time DH.) Arraez, Correa, Gallo, Buxton will get the bulk of it (30-40 games) and Polanco, Larnach, Kiriloff, ect will get the leftovers.
It's not necessarily how I would handle it, but I believe it is the reality.