mechanized infantry origins of TD
Aren't the Tank destroyers a logical result of the advent of mechanized infantry? The US had rifle units on M3 halftracks, so it was logical to give them mobile AT weapons, ergo the M3/75mm Gun combo, wich was the AT equivalent of the M3 mortar combo, etc...
Since the Riflemen were going to operate closely with the tanks, why not put the AT guns on tank chassis? And since said chassis was big, why not use the biggest AT gun avaible at the time, the 3'' that looked so good on paper, until the ammo designed for it proved to be a bit of a letdown?
When the Sherman was introduced, it's 75mm Gun was a perfectly capable tank-killer averywere except Russia, and in a Tank Vs Tank engament the Sherman was better than it's designed opponent, the PzKfw III with the 50 L42 GP gun.
So the idea was not that tanks wouldn't engage in Tank Vs Tank actions, rather than the Infantry would be supported by dedicated antitank units, and wouldn't require Tanks for that job.
The germans in Africa had been using their AT guns (including SPG versions) as their primary Tank Killer. The problem with the US was that they went one step further, and having created a dedicated TD force, regarded the Anti Tank capability of their tanks as secondary, failling to introduce a 90mm armed tank medium tank (The T25 would fit the bill nicely).