May isn't that kind leader and seniority is not a good reason. She is there to kick ass and chew bubble gum. She is the cavalry and she knows that. Her thought process is too narrow, easily out of her depth but she is self aware of this willing to deferrer to specialist. She is comparatively too amoral, I remember her shooting a kid or something. Even if offered I would expect her to turn it down. If you want someone to lead a strike team, you can't find better.
Which leads into Skye who is very open minded but wasn't made director because Coulson believed that the person at the top needed to be in control, to put their foot down with an equally good reason. Not because he thinks someone is the fucking devil. May handled it better. Mack never earned enough respect to be effective, uncharismatic, un-inspirational, so narrow. He has his moments but they are few.
Also season 5 didn't have many people to choose from, SHIELD was all but gone.