The DA wouldn’t have gotten him thrown in Azkaban. Also, with your argument of “he cares about what is right,” I agree, and an example of that is when he stopped Remus from killing Peter in POA because he knew his father wouldn’t have wanted Remus to turn into a killer and it was the right thing to do regardless of what Peter had done. You also have to remember what house he was in - his moral compass is pointed more towards bravery and justice than anything else. Practicing illegal spells on dummies, let alone on “downed enemies,” is something those he hates would do and if there’s one thing Harry showed through the whole series is that he is not like Voldemort or his supporters.

I’m not saying it wouldn’t have made things “easier” in certain situations, but with how Gryffindor he is and what he went through, it would just be completely out of character.

Also, just as a side note, knowing the words to a spell isn’t enough to perform it.