I'll accept that without a qualm. The threshold, IMO, is the question, here. Does the .45 ACP (or, indeed, the .455 Webley) meet it? Or does a hotter round?
That's the issue I'm getting at: would (could) the Army ask for a hotter small-caliber or a (less hot, but hotter than OTL .45 ACP) larger-caliber round? Or is the .45 ACP the best compromise?
For the situation the US Army found itself in the early 1900s the .45 ACP is close to perfect. A hotter, smaller caliber cartridge makes sense if:
a) They were expecting to use it in a submachine gun (high chamber pressures = larger muzzle velocity increase from longer barrel)
b) They were expecting opponents to wear body armor
c) They were expecting lots of action against mounted cavalry
Of the three, only c) was plausible at the time, and even then rifles and bayonets were considered the primary counter to cavalry for the average infantryman.
The only problems the .45 ACP had as a pistol cartridge were excessive bullet drop and inadequate penetration against heavily clothed opponents in cold weather. As US troops found out in Korea, multiple layers of cotton and silk, with the outer layers frozen, make for decent armor against low velocity handgun bullets.
The French ignored the first principle of engineering design: "DO NOT REINVENT THE WHEEL!". I hope you do not include among France's "really good weapons" the Chauchat LMG and the Lebel Model 1886 rifle.
Don't knock the Lebel. The cartridge it fired was powerful and the rifle itself held 8 rounds in the magazine even if it was a tube magazine. Lee-Enfield aside, how many other bolt action rifles of the period could say that? That being said, continental European handguns of the period (outside Russia) tended to be underpowered because they were more badges of office than actual fighting weapons. Officers with handguns were supposed to
lead the troops with rifles and machine guns who did the actual fighting.