In the same book Frost goes on to talk about a Platoon at Arnhem bridge armed to a man with Bren guns, taken from fallen or wounded comrades. My point being that while there is an agreed start point for weapons distribution in any army down to section level, that probably will not remain a constant in combat. On a previous post I talked about a resent read Battalion , Seaforth highlanders in action, well when clearing an enemy position at close quarters, automatic weapons and grenades were the go to, not rifle and bayonet for very obvious reasons. Also whilst this is Africa, Germans and early/mid war, the British army as the war progressed introduced more automatic weapons to infantry, because in fire fights with a force of broadly equal size they were being beaten for sheer rate of fire, so the nco may have once been the only guy in section with a Thompson or Sten , by late 44 half the section may of been armed so.
No arguments here Alan, but as these are not British paras in '44, but German infantry in '42 or so, there's really no point of all the SMGs. Soldiers got those weapons because they were needed in close quarter combat. The desert was characterized by long range encounters, and soldiers are usually clever in the way that they get what they can use, which is in this case a nice handy Kar98k.