Ammo is loaded via back (even when in limbs, per rule), so presumably it is quickest way to remove it all at once. I mean, one dumps ammo in the event of elevated heat or weak armor and you need to get rid of it all quickly. Also, relative safety: Ammo getting dumped from elsewhere than back would risk it getting hit and blowing up, 'Mechs usually do face the enemy rather than show their back to them.
Through-weapon probably isn't an option usually. In case of caseless ammo like missiles, there is no ejection port, and they need rear door or something anyway. Or if the weapon is damaged, you need an alternate way to remove ammo.
The lack of exact torso location (or location at all, or weapon affecting thigs) is presumably abstraction and simplification of rules. Very early rules for BT didn't include the option at all after all, so perhaps it was added back when things were "quick and dirty" (as writing went).
EDIT I wrote: (Caseless ammo for ACs happens only with caseless versions of ACs (not ammo itself unlikely in earlier editions of BT), and i think no canon design uses such at the moment.)
But it seems i forgot how things work at the moment. It seems when using TacOps rules, a player could designate ACs as using caseless ammo but this prevents alternate munition usage.
