I said dumb, you said cowardly.
And the best general alive wouldn't be in melee. He'd have others do it for him.
I think this is a case where D&D is much more like One Piece than it is like real life.
In real life, the greatest general alive isn't a particularly fearsome fighter. She might be reasonably bad-ass just from coming through the ranks, but even so, no personal military skill can compete with a mass of troops, so her tactical skill is far more important than military might.
But in One Piece, the great admirals and generals are all personal bad-asses, with superpowers, pussuant kung fu, etc. In that world, it's possible for a person to become much more militarily important than hundreds--even thousands--of average strength troops, so the soldiers that are promoted and promoted until they can't get promoted any more end up being valued as much for their power as military forces of nature as they do for their tactical skill; either way, nobody can reasonably be in a position to give them orders, so they're in charge (and the same is true for the top pirates, of course).
Similarly, in D&D, the better you are at -anything-, the better you are at combat (even if this is less a law of nature in 4e. Even so). And as importantly, it's -possible- for someone to be worth a hundred "normal" troops; that's normal for a paragon or even epic threat. So you better believe the greatest general would be up to mixing it up; if they weren't, they wouldn't be the greatest general -- not in D&D.