The M73/M219 and M85 tank MGs, as well as the M1 and M19 cupolas on M48 and M60 Pattons. The M73 was a disaster because the receiver was too small and light and the action too fast so it would wear very rapidly, M85 seems to have been too complex and unreliable too. Considering that FN MAGs were already available and would be adopted 20 years later, and that M37 (M1919) MGs were reliable and could be converted to 7.62 NATO, and finally that 7.62 tank MGs don't care much about size and weight, the US shouldn't have been using a crap MG for this long.
The M1 cupola was downright atrocious, too small, not good enough observation, the M2 Browning is on the side and insanely hard to reload and if you reload it you only have 50 rounds (granted, some genius apparently made the longer belts work, somehow). The M19 was a bit better but still suboptimal. I also have serious issues with a cupola 12.7 at this point because it's pretty much useless against planes, heloes would just wander out of range with missiles, the only benefit is extra performance against infantry behind cover but frankly it would be more ergonomic to have a 7.62 operated by either the commander or the loader on top if needed, and a 7.62 or 12.7 coax to deal with infantry in cover (or just use the freaking gun and stop issuing weak HESH or HEAT for the anti-inf role and make proper HE!).
Last reason I dislike that kind of cupola: the commander is supposed to command/and/or range, stop giving him more to do. A tank with a commander that observes the battlefield and commands is better than one whose commander is shooting all the time, which is frankly no better than a 2-man turret with some extra dude shooting an MG and only a gunner and loader. Bonus point: getting a regular low-profile cupola (whether it counterrotates or not) will reduce the height of the tank, reduce weight by several hundred kgs, reduce torque on that side of the turret, and it avoids getting the commander killed by a hitcin the cupola.