My personal opinion about rimless straight-case pistol cartridges in a rapid fire rifle is ummm...problematic from the get-go.
What do you consider "straight-case"? All the rimless pistol rounds I can think of have some degree of taper. Some more than others, but even the "straight" ones do have a small taper. The "straight" .30 Carbine and .45ACP (as well as the less straight 9mm Luger) have worked well in MILLIONS of carbines and SMGs, for longer than most of us have been alive...
The major issue I see with almost all pistol cartridge carbine designs is that they are built around the concept of magazine cross-compatibility with pistol sidearms--and so the carbine's manufacture is governed by making that receiver and feed work with what was intended for a pistol slide.
I won't disagree that building a rifle/carbine to function well with a pistol magazine is a tricksy task. But it is the design engineers responsibility to do it, and do it right to begin with. And its the production guys and QC's job to ensure that the design is made correctly. MOST of the time, the design is adequate and problems are due to construction flaws, but not always...
I'm old school about many things, my favorite PCC was my Thompson M1927A1. Despite its flaws, it was just FUN!! (IF you could LIFT IT!!!
) Not built to take any pistol magazine, that one. (the Tommygun "pistol" does use the same mags, but the carbine came first, so the pistol uses carbine mags...)
My other PCC is a Calico, and its top mount helical 50/100rnd mags are so far outside the usual design it really doesn't fit the "pistol mag" discussion, though the carbine and the pistol do use the same magazines.