I agree.  I would never add Drama as a genera to a War movie.  In fact there're no genres I would add Drama to 'lower down the list'; (except Television or Animation, which aren't really genres anyway).  I treat Drama as the default one to use if nothing else especially fits, although I will add other genres 'lower down the list' if a Drama contains smaller elements of others.

I try not to have more than two (or occasionally three) genres per movie or TV series.  I have a sort of primary list I try and pick from for the first one in the list and then add one or two others if needed; (plus the 'non-genre' genres if I want, although only Television or Animation get to go at the top.)

For M*A*S*H I'd put Comedy first, then War.  This is because it's really a comedy set in a war setting, rather than a programme about war that's funny. (I realise that makes no real sense, but hay, I'm left-handed, so that's how my brain works.)

Kramer vs. Kramer is a straight Drama, nothing else.

Saving Private Ryan and Platoon are both War, but also Action too.  But I'd put War first, as Action always feels more of a 'mood' or film design, than a 'type' of film.  In fact I think I'd rarely, if ever, put Action as the first genera in the list. 

When I watch a film I actually quite enjoy the process of trying to pigeon-hole it into a genre.  I think I fall into the 'lumper' rather than the 'splitter' group.

Agree with both of you! Drama is more of a "catch-all" when nothing else fits...

I would use drama for films where the war is just the backdrop and not the main focus of the story.

For example I recently watched Tolkien. It features scenes from the first world war, but at least three genres would come before War in my genre listing: Biography (one of my custom genres), Drama and Romance.

The way i use it is first comes the medium (Television, Documentary etc), then the theme (Science Fiction, War, Fantasy etc), then the genre (Action, comedy etc).

Only custom genres i use, are post-apocalyptic, space scifi and asian.