Weighing in at a half ton/quarter ton a piece, the 'machine guns' mounted on mechs and tanks are less actual machine guns and more micro auto canons.
Problem is when the writers talk about MGs as if they are M2 Browning or a Kord-12.7 rather than something closer to it's stated weight such as the GAU-8 Avenger or a MK44 Bushmaster. While small compared to a standard AC, these are still big guns and the only reason have short range because of the armor in the BTU ignores anything not traveling at it's highest velocity. (These guns can probably still splatter infantry from across the map while bouncing off armor like hail stones) The Rapid Fire rules also hint at MG's GAU-8 Avenger like nature as the weapon doesn't heat up unless the Mechwarrior holds down on the trigger longer than that 1 short burst, firing more rounds in the same relatively short amount of time (1 turn)
Should Mechs ignore small arms? Absolutely and do so in fiction (unless writers decide otherwise because plot) but the game made some abstract concessions in order to make combined arms more appealing. For myself, I consider each PBI squad to be carrying 1 squad support anti-mech weapon among then to justify their TW numbers. They are not just spraying their space AKs/M4's at the towering armor and hopping for the best but firing one carefully aimed shot from their biggest gun (possible modular and carried in pieces)
Should both MGs and AMS both be used as point defense similar to Naval CIWS? Why not? It would justify the insane ammo counts and give both weapon systems more utility on the battlefield. Yes, I'm saying the Piranha should be both a walking war crime and a walking iron dome AMS platform *evil laughter*