I don’t know, off hand, of any further studies regarding differences in the performance of brass and steel-case ammunition, but there certainly must have been some.
Steel-case pistol ammunition really came into wide use about 1941 (1942/43 in the US in .45). There certainly was some use prior to that. Steel-case 9 mm
Was made by both Cleebron and Spandau, I believe, in the WWI period but specimens of that ammunition are so rare today, unlike brass case WWI German 9 mm which is often found, that its use must have been absolutely minimal. I think I have actually handled only one or two German WWI steel-case 9 mm rounds in 50 years of cartridge collecting. I have never owned one.
There were problems with the German steel-case 9 mm. All of the packaging with “Holsenklemmer” and “nur im Maschinenpistolen verschiessen” (Shoot only in Machine Pistols) are proof of that. The latter label did NOT identify ammunition too powerful for pistols, but rather ammunitiion that was not reliable in precision-fitted weapons like the P-08. It doers, seem though, that it was successful in weapons like the MP-40 and the various other German and foreign Machine Pistols pressed into service by the German Armed forces.
Regarding American steel-case .45 ammunition in Thompsons, I have no experience at all with the M1 or M1A1 Thompson. I have never shot one. I have had some experience with the M1928A1 Thompson, however, as well as the M3 and M3A1 “Grease Gun.” I have shot hundreds of rounds between the two types (only one specific Thompson, to my knowledge, although since my many firing sessions with it were at the courtesy of a Federal LE Agency, there might have been more than one over the three year period that I participated in the range activities), but several different M3s during military service - all peace time so NOT under combat conditions, admittedly. I do not remember ever having a malfunction. Virtually all of the ammo fired was, of course, from Evansville Chrysler. At one shooting session with the thompson, we fired a burlap bag full of that ammo, so dirty that some of the headstamps (yes, I ALWAYS look at headstamps) were not even legible for the “gunk” covering them. At that session, there were zero malfunctions, with the ammo fired in about 6 or 7 different 20 and 30-shot mags, and two 50-round drum magazines. All of this Thompson shooting was done in the 1970s and 1980s, as I recall, so the ammo was already approaching 40 years old. The M3 firings were down in second half of the 1950s and early 1960s. I fired a very few rounds, perhaps a single magazine half full, to demonstrate an M3 and a Store-sponsered Sunday picnic/shoot at a San Francisco Bay Area Police Range, where local authorities and MG dealers kindly provided some SMGS for the enjoyment of our guests, but I did not load the magazine and have no recall of the ammo used. It may well have been commercial, brass-case.
I have, with both SMG and Pistol, developed a huge respect for the quality of American Evansville Chrysler steel-case .45 ammunition. I used to keep an older GI .45 just for shooting what I acquired beyond collecting needs because it was corrosive, and I did not care to shoot in my match pistols or personal defense guns. Simply a matter of cleaning. As far as dependability, I would not have particularly worried about having it in a “defense of life” situation.
I have had my ups and downs with German steel case ammo. I don’t consider any of it particularly safe to shoot today, due to rotting of the case from the inside, in which instance a cartridge can appear mint on Monday and be sprouting rust all over it on Tuesday! I am sure it was adequate for the times in which it was used, but the passage of time has not shown the shelf life of the American .45 ammunition, by any means.
I have never had much trouble with COMBLOC steel-case ammo, most of it post-Korean War or even post-Viet Nam, and in 9 mm Makarov, the Chinese ammunition, in particular, has proven to be accurate and absolutely as reliable as military or commercial pistol ammunition I have ever fired.
Just some personal observations, for what it is work.