I saw in a comment in a thread that briefly mentioned that soldiers wouldn't follow doctrine as tank destroyers. Can someone elaborate? I felt like this might be better answered in its own thread.
United States tank destroyer doctrine, on paper, held that the tank destroyers were to be kept back as a reserve, and brought forward quickly to counter large formations of spearheading enemy armor. The tank destroyers would use their speed (the only tank destroyer that exemplified this part of the doctrine was the M18 Hellcat, with a top speed of 45 to 50 miles per hour on hard road) to obtain ambush positions, fire on enemies, and quickly relocate. The only battle where the tank destroyer force fought as intended was the Battle of El Guettar, where a large formation of German tanks attacking on a narrow front was broken and turned back.
The doctrine did not mean that tanks were not supposed to fight other tanks, a popularly-believed myth. In US pre-war (I say this as the Army had to improvise "on the fly" when the Germans wouldn't play by the book!) tank doctrine, medium tanks are primarily the "assault" force, supporting infantry by knocking out enemy fortifications, guns, and tanks threatening the light tanks. The "exploitation" force is light tanks, which use their speed to move into the enemy's rear areas. The roles of light and medium tanks can be interchanged. FM 17-10 and 17-33 make several references to the role of the medium tank, noting that it is to assist and even take the place of the tank destroyers when necessary, and protect the light tanks from the attack of hostile tanks.
In reality, tank destroyers were often used as mobile artillery or infantry support, attached to infantry or armored divisions (this runs in direct counter to the doctrine; tank destroyers were not supposed to be parceled out, but employed in their full battalions) Since US tank destroyers generally had light armor and open-topped turrets, they were vulnerable to enemy guns and launched or hand-thrown weapons. Many tank destroyer crews improvised turret roofs of steel plate and added extra machine guns to their turrets. Infantry commanders, when employing their attached tank destroyers, often went by the logic of "Well, it looks like a tank, and that's all I've got".