You'll probably find the Sherman was intended to go tank-on-tank when it was designed in 1942. When it was designed the best the Germans had was the Panzer IV Ausf F/2 which the Sherman could match.
The Sherman wasn't intended to support infantry. This is always wrong when concerning tanks, especially those as mobile as the Sherman, that they are designed to support infantry. That is wrong, the Sherman (as with all British classified Cruiser tanks) were designed to entact deep breakthroughs and fast advances. With the British finally getting the idea about armoured divisions in N. Africa 1942 and passing the information to the Americans - both countries realised that tanks were supposed to be able to take on everything and everything supported the tank, not the other way around. That is why everything from infantry to artillery ran on the internal combustion engine, to keep up with the tank.
You're right though about the mobile AT platforms, the Tank Destroyers. Tank Destroyer companies (consisting, in US Armoured, of M10s, M36s and M18s - generally) were attached to armoured advances and were tasked with hunting enemy tanks to clear the way for the cruiser Shermans.
The Pershing was actually delayed because the US Ordance Department stated that a tank as good as that with a 90mm cannon will influence tank crews to hunt enemy tanks, and that's a job of the tank destroyer...silly-silly people.
I would like to make an addition to the last post, a German counter-offensive around the Polish village of Borowe in Jan. 1945. Elements of 2nd Byelorussian Front were counter-attacked by Panzergrenadier Div. 'Grossdeutschland' and took the village under intense fire from ISU-152s of the 390th Guards Independant Artillery Regiment. This is long-range direct fire on the defensive, also reminding you all that the Germans were conducting counter-offensives all the way up 'til the fall of Berlin. A local counter-offensive is all part of the grand defence.
On the offensive, 1st Ukrainian Front's break-out from Sandomierz Bridgehead over the river Vistula. Marshal Konev used ISU equipped regiments to increase the initial artillery barrage and when the assault troops moved forward, poor visibility disallowed any air support or close artillery support. So, the only direct fire was given by the ISU-152 and ISU-122s advancing with the assualting infantry.