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Yes, but will you need all those weapons in a single battle? The ability to switch out gear at a moments notice or to even craft your gear to the situation is useful. Also it reduces the net weight of your mech. While an armless model may have the advantage of no flailing apendages I think it has been shown that arms are an advantage not a disadvantage.
Now, here's where I don't see any hands, but Battletech may not be the best example, given that the only common hand-held weapons are melee, so an anime example would probably be needed. Given that I haven't been able to find one yet, however, leads me to think that the hand-less main combat unit is fare more common on this side of the Pacific.
Off the top of my head, I can think of the following Battlemech's that have hand-carried non-melee weapons: Stinger, Phoenix Hawk (a Robotech rip), Griffin, Wolverine, Charger, Battlemaster, Vixen. Battletech's explanation on pumping electric output from the engine to all weapons that need it contradict the theory of hand-held weapons though, which probably explains why you don't see many hand-based non-melee weapons in BT, and the ones you do are almost exclusively some of the earliest designs. The best explanation is that they're fed power through some kind of link cable. The weapon can be abandoned (blow explosive bolts on the link and drop the gun) but can't be wielded again except as a club.