For me, some anime almost makes the mark: Code Gease almost got it right - in fact, it's first third or so was awesome. 'Knightmare Frames' were a decent embodiment of mass-produced walking tanks and the 'hero mech' Gurren made sense. The use of what amounted to rollerskates for extra manoeuvrability *almost* made sense, but they went seriously over the top with the insane speeds and turns they could pull off.
Then they went down the whole 'children proving themselves with mech piloting ability' route ALL anime likes to go with, then the magic mechs turned up - you know, the ones with handguns that could blow away the moon and that could fly with a small backpack. Yeah, the end got shitty to the point that I was wondering why on earth either army even used Nightmares anymore, seeing as how many super-special-awesome hero mechs there were :/
Full Metal Panic also had some nice, chunky almost Western designs, but when you see a MECH peeking around a corner, clutching an assault rifle, before dashing out and gunning down a guy - sorry, mech - down the far end of a corridor you realise that the mechs are entirely secondary to the action here, as opposed to being the focus of it. That's the wrong damn was around :/
Armoured Core is pure win to play, but the problem is that you could replace the mech with a dude in a suit or just an anime dude and you could get away with exactly the same gameplay - there's practically nothing there that makes it about giant robots other than the art.
Mech Warrior gets it beautifully - titanic death machines that move at conceivable speeds equipped with weapons that feel as powerful as they are, with the traits of each mech visible from its appearance (as in, that rifle isn't going to turn out to be some super-mega-deathray cannon, it's just a huge fucking cannon). Have a look at the opening and tell me you can't see the epic that these mechs bring.