. . . I'm having a hard time believing there could be upwards of 40 million braces out there.
Same here. I've seen enough to recognize that they're "in common use" and can readily believe they number well into the millions. But
40 million?
While there's well north of 20 million AR-pattern firearms out there, I'm sure the preponderance are rifles & carbines. Add in other likely candidates for a brace (AKs, Skorpions, B&T, HK, etc.) and I'd still be surprised if the total of braced pistols reached 40 million - that would mean about 1 in 10 of all privately owned firearms was a braced pistol.
I don't think so.