Indeed, Harry should reconsider his picks of Dumbledore's Army to actually fight - Hermoine is a bad pick; Neville is a good one.
I kind of agree with what you're saying, but not entirely... I think Harry may have learned (or if he didn't, he should have) that the people he might not immediately consider to be worthy to have around in a fight might actually be the best. After all, in the beginning, he wouldn't choose Neville, Luna or Ginny if he had to pick three people out of the DA to join him, Ron and Hermione. But those three kept their heads better than both Hermione and Ron.
Hermione isn't useless, though. Even though she may not be good in a battle sense, she very much understands people, and she has extraordinary problem solving skills and is good with strategy. That may be just as important as being good in battle.
In truth, every one of the students have their strong points. Neville, as we're coming to find out, is made of tougher stuff than we originally thought, and he seems to have a real hunger to prove himself. Luna, for some reason, can live with her head in the clouds, but be grounded enough to be reasonable in hectic situations. Ginny has sheer power and is stubborn, making her a tough opponent to knock out completely. Hermione, as I said before, understands people and is excellent at the problem-solving. Ron is incredibly loyal, and while he's no great shakes, you couldn't want a better second. When you put them all together and they're working as a team, that's one force to be reckoned with.
About one of the trio dying... I would be sad to see any of them go... But, oddly enough, my least favorite character of the three is Harry himself.

I feel like I really understand Hermione, and Ron (in the books especially) cracks me up. Sometimes I just feel like, if I were face-to-face with Harry, I would have to hold my tongue to keep from telling him to go throw himself a pity party and get it over with...
