Delph works well in that formation and should keep his place, played smartly that could take down good teams.
People generally over estimate how good a lot of the big teams are, its a big failing of the England team in how much undue respect we tend to show to teams. Look at how we played Italy, showed so much respect to Pirlo who really did not deserve it which showed when he had Costa Rican and Uruguayan midfielders swarming all over him the next two games and was very poor. England don't currently have the players to stand toe to toe with the very best, but the world cup showed you really don't need that. Delph is not a top player but neither were most the US, Chilean or Costa Rican players who scared the life out of better teams than England.
England's strength should be we have some potentially world class counter attacking talents, our midfield isn't going to destroy or control teams but what they can do is bloody their nose, people like Delph are perfect for that. Look at the Chile team that played against Spain, on paper the Spanish midfield beat them in every conceivable way but the sheer energy of their team forced them into mistakes and didn't let them into the game.
This England squad isn't going to win Euro 2016 but with clever tactics (not trying to out pass better teams, not standing off waiting for them to cut through you and instead get in their face...) we should be a lot more of a threat than we looked at the world cup. Unfortunately that's not really Hodgson's style but hopefully he too learned a lot of lessons from how Chile and Costa Rica took down superior sides.