For the next two to three weeks, Wright will play as a designated hitter, because he’s that far from being able to throw. And, Wright isn’t fast enough to run the ball across the infield. This should also limit talk about moving to first base because he has to throw from that position, also.
It’s not alarming now because it is a long spring training and the Mets have depth at third with Jose Reyes, Wilmer Flores and even Neil Walker, if pressed. It is better to have Wright later rather than risk additional injury and be without him longer.
As for Wheeler, he had elbow tenderness but has thrown two strong bullpen sessions since. The Mets currently see him as the fifth starter rather than a bullpen arm, which is fine as long as they stick with that plan.
Spring training is to get ready for a long, grueling season, but there’s written in stone all players must be ready for Opening Day.