Biggest problem for the 76mm was lack of tungsten for ammo. The AAF had the War production Board priorities for tungsten for machine tools. Very little was available to Ordnance for ammo. Tanks had very, very low priority under the WPB. The Chrysler Multibank was an emergency stop gap because auto engines were available while AAF scarfed up all the radial production and the USN scarfed by the diesels. Tanks only got the Ford GAA because the AAF decided to go with Packard-Merlins leaving the Ford production to the tankers. The 76mm and the 3inch were adequate guns with inadequate ammunition.
To a degree, yes, but it is too easy to use tungsten as a cop-out. The 76mm also was problematic because the Armor Force preferred the HE performance of the 75mm and never really changed there mind on that because Ordnance never developed a lower velocity HE round for it as the Germans (and eventually British for 17-pdr) did. Nor was "tungsten" the only solution. Proper heat treating of the AP projectile and more work on the fusing or discarding the APHE entirely in conjunction with improved heat treating would have been about as good. It is significant that when the Navy tested 3"/76mm AP performance after the end of the war they found the 3" AP produced to Navy specs performed well, while the 76mm consistently shattered. On top of that, the Armor Force consistently shot itself in the foot. Even Jake Devers, perhaps the smartest general to achieve his rank during the war, bollixed the 76mm acquisition, by reversing himself on the M4A1 (76mm) and so allowing the TD Command to scarf up available production for a year.
Nor is the engine problem so cut and dried. Prewar Ordnance settled on gasoline radials for its tanks, with a diesel radial back up. By early 1941 it was obvious the Air Corps plan enunciated by Roosevelt would consume all excess production of radial gasoline engines, so the diesel backup was activated...and the Armor Force accepted, only to reverse itself six months later - NO RADIALS and NO DIESELS wanted...oh, but maybe we'll accept gasoline radials until something else comes up. That left Ordnance scrambling for ANY solution after expending some seven years developing the radials. Yes, the A57 was an emergency stop gap, but so was the Ford GA series, the GM twin diesel (oh no, diesel!). BTW, the AAF did not "decide" on Packard, the original manufacturer was Ford, but Henry famously reneged on the deal because it was to supply the British...OTOH he was clever enough to make sure the Rolls-Royce drawings and specs were examined in minute detail by the Ford engineers to give them a leg up on their own engine.
In any case, Armor refused the A57 because the pilot design was so problematic, even though the engineer assessment was that with tweaking it would work fine, which is what happened. In the end, the only "problem" with the A57 was its size and weight, it was actually the most reliable of the engines. They refused radials because after seven years of developing 1st echelon maintenance requirements for it, they apparently thought that was too much for the crews. They refused diesels because, well, apparently they didn't like the smell, because there was never a clearly enunciated reason against them that made any sense. That left the GA-series, which meant they hitched themselves to a development project that was a fraught with problems as the A57, where production was too limited until late 1943 when development was complete, which meant that the American tankers received Armor's preferred tank engine in the fall of 1944...and then in winter 1944/45 begged for tanks with any kind of engine to fill shortfalls, which meant American tankers were driving M4A2 and M4A4 in the spring of 1945.
Meanwhile, the Marines had zero problems using the M4A2.