Yeah I agree that a Raiders tone would be perfect for this. But I can see Steve's doubt not coming from the horrors of war necessarily but the absurdity of life that he's now forced to live.
His initial goal is to do his part and join the service as he says he has no right to let other men die while he sits back. He doesn't want to be this hero everyone looks at he just wants to be another soldier like Bucky who's doing his job. After the super soldier serum and Erskine's death, however, all of this changes. He's now a literal one man army and has the hopes of his country riding on his shoulders. Instead of fighting in the trenches he's now facing off against magical Nazi supermen like Red Skull and HYDRA who now have possession of a weapon that literally rewrites time and space. Steve's reaction of self-doubt is completely realistic I say and he'd be an idiot to not contemplate it.
