M4A3 (75mm): Unable to stand up to late-war German tanks, but kept in service by stubborn Army officers. After they failed make a dent in the Ardennes Counteroffensive, High Command ordered all new Shermans to be 76mm armed.
They couldn't really replace tens of thousands of Shermans in service overnight. The 75mm shermans were supplemented by 76mm right from the start of the invasion of France, which seemed like an appropriate solution given that the 75mm had superior performance vs soft targets, which is what they spent most of their time fighting, infantry, bunkers, at guns etc. 75mm did just fine against the assault guns and PIVs and what not. Panthers were the only common vehicle that a 75mm has trouble with, but even a 76mm has difficulty penetrating that frontally unless they're using the HVAP rounds that were not commonly distributed to non-TD units until very late in the war.
Decision makers were getting conflicting information from units based on experience in Italy and North Africa, some saying that they didn't think they needed heavier TDs and what not. It's pretty complicated I guess. Wasn't until they started encountering tons of Panthers that they really started rushing the 90mm stuff into service.
I guess it's a question of whether you consider something obsolete when there is something that can decisively outclass it, even if it's relatively uncommon or other factors dilute its impact. The 75mm Sherms were doing fine on average, even if we now tend to have a warped perception of these helpless American tankers getting slaughtered en masse by Big Cats.