Historically the development of the Panzerfaust was a method to produce an alternative to having to use magnetic mines, AT Rifles, or other expedient weapons to defeat enemy armor. The early models had extremely limited range and poor accuracy, as well as taking a while to get into service and set up production, while being relatively heavy. At the same time the German army refused to invest in AT rifle grenades, unlike other nations and the Waffen-SS:
http://www.inert-ord.net/ger03a/gerrg2/mod4661/index.html
http://popernack.com/library/library.php?aID=10&xID=1
What if the regular army had instead of developing an entire new class of recoilless weapons (the Panzerfaust was not a rocket) instead opted to develop HEAT rifle grenades like all other nations and the Allies did post-war? They weighed a lot less and were longer ranged and in fact somewhat more accurate than Panzerfausts prior to the very late war versions.
Having say a French style bullet trap design would be very easy to use and very effective, more effective than the Panzerfaust pre-1945 models:
https://en.wikipedia.org/wiki/AC58
I'd argue having something like this in service even based on the 50mm mortar around (they used an 81mm mortar round with a very high penetration value for the PAW600) would have been do-able in time for 1941 and been more than capable of giving the infantry squad a means of killing enemy medium tanks at greater ranges than the Panzerfaust at lower cost and much earlier in greater numbers at lower weight.
What sort of impact would it have had on the war to have the average infantry squad capable to knocking out T-34s/M-4s from 200m or more away, while not having something like the Panzerfaust inspiring post-war designs like the RPG?