"Tank destroyers seem to me best suited on the defense where their area of heavy armor and gun can be pre-sited on a likely fire axis and the rest of the vehicle as hull down as possible."
As originally envisioned, American tank destroyers were expected to deal with German tanks operating in blitzkrieg fashion using the kind of fast moving tactics that had worked so well in Poland, the low countries, and in the open stages of the Eastern Front war. In those tactics, German tanks punched through opposition and ran in front of their supporting infantry and artillery, effectively operating as cruiser units.
Purpose built American tank destroyers were designed to counter German tanks operating mode by being fast and mobile, which would allow them to engage and disengage at will, and also, as you mention, in pre-sited firing positions in a defensive mode. Unfortunately, it rarely worked out like that during World War II.
By the time American units entered the conflict wholesale, German tactics had changed dramatically, and were operating increasingly in a defense in depth mode. As such, American tank destroyers rarely got the opportunity to operate as originally intended, and it was then that their design limitations became glaringly apparent.
Besides the light armor, many American tank destroyers had open-topped turrets. While great for visibility, it left the crew vulnerable to infantry and air burst artillery and, in fact, many tank destroyer crew casualties were caused by shrapnel when they were put into combat situations where German armor was supported by artillery.
The same was true when tank destroyers were used in supporting attacks against German held positions -- the light armor and open topped turrets were vulnerable to just about everything above small arms.
"Are you talking about the lightly armored tanks with big guns or the half tracks with artillery?"
The "half-track with an artillery gun stuck in the back" was an expediency design, and was virtually never used after the invasion of Sicily. It was effective against Italian tanks and early German tanks, but it was slow, vulnerable to return fire, the gun had very limited aiming capabilities, and the gun's performance was quickly superseded by increasingly heavily armored tanks.
Most of the M3 Motor Gun Carriages in Europe ended up being used as self-propelled artillery or simply having the gun yanked out and the half-track returned to its originally purposes.
They were used with greater effect by Marines in the Pacific, where the rather lackluster ballistics of the 75mm gun was still more than enough to deal with Japanese tanks.
