PSH was so much better than the MP40 because it was just fully dedicated to being a bullet hose
That was a mix of things. It was what the Soviets could mass produce quickly. It was going to be widely issued to moderately trained
soldaty for the sole purposes of providing suppressing fires in either advance or in retreat.
The "PapaShah" would empty its (very hard to load) drum in only a couple of seconds. The stick magazines vanished even faster. PPSH were meant to be issue with two factory-fitted drum mags, which were serialized to the weapon. The drums did not transfer well between firearms. (Drums are a pain to carry, too.)
The Soviets replaced the PPSH-41 with the PPS-43 as quickly as they could, too.
The cyclic rate of the MG-42 was 1200 RPM. Why
The Germans were committed to the idea of a Universal MG, that could be used across the entire Wehrmacht. Which is a tall order. Aviation use is very different than ground use. The target presentation is much, much shorter in aviation combat. You need ridiculous rates of fire to get
any rounds on target. That brevity also allows some balance in holding to a limited number of rounds carried as well.
While the idea of a UMP is intriguing, even the Luftwaffe adopted other weapons.
Now, there is a fascinating War College monograph on how the Germans may have selected the ridiculously high rate of fire for the MG-42 as a result of massed infantry attacks by the Soviets. The Soviet infantry tactics are complicated, especially during the Great Patriotic War. They did not respond to the measured, calculated tactics of the Reichs Heer, and an answer was required.
Has anyone ever heard a comparison of the M-14 fired in semi vs full auto from a soldier who was trained on or carried one?
Yes. It was a pig. Circa eight pounds is too light for full auto 7.62nato fire, unless the intended desire is a conical effect. The FAL is only slightly better, for having a slightly better in-line design.
But, functionally, trying to make every rifleman a Squad Automatic Gunner is less than tactically sound in the first place--barring some extremely specialty units. (The jury is still out on the USMC use of IIAR as a Squad weapon.)
Rates of fire have very specific uses in battle. While similar in defense as in offense, but they remain specific. The ranges used are also significant; if less apparent at face value.
Riflemen operate in Fire Teams (which can be an
ad hoc or deliberate grouping). And typically operate at Rifle ranges (400-600m).
Fire Teams make up a Squad. Squads will have organic support out to just at the limits of rifle ranges.
Squads make up Platoons. Platoons will have a support Squad, which will give them the ability to reach out to right at double rifle range (1200-1800m). Individual aimed fire at such distance is generally not an option, so, indirect, automatic fire is appropriate (when not using mortars or direct-fire rockets).
Platoons make up Companies. The Company will have a Weapons Platoon for support of all the Company assets, which will range out to 2-3km or so, depending upon need.
Companies make up Battalions. Which can have all kinds of support elements attached.
Battalions are used to make up Regiments. Regimental attachments can be armor, arty, aviation, and the like.
Regiments then create Brigades; Brigades make up Divisions; Divisions make up Corps; from Corps to Army, and Army to Theater.
It's all too common to lose sight of the larger and focus on the smaller. All that organization exists because individual troopies are heard pressed to hump 40 or more kilos every step of every day. And because threats exist beyond rifle range. It can be very convenient to be able to call Brigade and get them to put some 155mm on target 8-10km down range.