The impact power of ‘battle’ rifle rounds is over emphasised in judging the effectiveness of a round. What the powerful rounds do is flatten the trajectory so the same sight setting will do for a wider range of distance. The pistol rounds will kill and injure out to as far as most soldiers ever fire but the drop over the longer distances make accurate elevation judgement more important and difficult. Taking the extreme version of arching trajectories, when the rifle musket took over from the smooth bore musket in the 1850s it became necessary to introduce long training to judge distances so that the sights could be accurately set. Trained professional soldiers could reach out to over 1,000 yards but the barely trained mass of soldiery of the American Civil War were largely incapable of using this facility and fired at ranges where the old smooth bore would have been pretty well as good.
Thus the advantage of the 9x25mm Mauser round is not that it hits harder (although it does of course) but that it has a flatter trajectory and simplifies the task of the soldier to make hits.
In addition the faster flight time reduces the effects of wind somewhat again making hits more likely within the limited range at which most engagements were made.
Now I am not competent to argue the cases for large or small diameter bullets in a blowback SMG but the 9x25 Mauser round existed since before WW1 so was a known quantity, already developed, it in use and is rimless. No new ammunition development or design work is needed. Ready off the shelf and easily loaded a little hotter for a new SMG than would be wise in a 1904 Mauser C96 pistol. It ain’t broken so no need to fix it. It is known to work and is up at the most powerful end of a potential simple blowback design SMG. Other than the, debatable, advantage of a small diameter bullet for the task, I can see no reason not to use it.