Barry is enjoying something of a renaissance at Goodison Park this season. So much so that it seems unfair to include him here. In the end he has been. Although this is more because, of the weaknesses that Barry's presence would compound than because, he is undeserving.
Never the quickest, Barry seems to have lost perhaps another half a yard of pace over the last couple of seasons.
In an England central midfield that is already lacking pace Barry's presence simply makes the engine room of the team to slow. At Everton this isn't too bad as Martinez has surrounded Barry with younger legs leaving him to play the anchor man role. For England though he would likely be lining up with the post-30 somethings Gerrard and Lampard.
Imagine a midfield three including Barry, Gerrard and Lampard playing together in the humidity and heat of Manaus against Italy. It doesn't bare considering.