Like many things in a presidency; this is clearly partially - probably largely - guided by external developments. Sure, the president gets more say that anybody else, but I'm skeptical you can ascribe too much blame (or glory) to the outcomes here; at best you can look at the details, and see if in a given situation (ideally in retrospect) a president made the right choices.

I don't think Trump was tested in this area, and I don't think most wars were trivially the fault of the presidencies they were started in (sure, some exceptions like the most recent iraq may jump to mind). I mean, "just don't participate" is also equivalent to ceding influence to whoever feels like a bit of shelling would do them good, so that's not always a good choice - under the assumption that the US (and world) was well served by some measure of imposed order.

Course, maybe I'm misinterpreting who had agency in those situations - do you think it's largely presidents' at fault for for the post-WWII military engagements?