This is a rare case where that cycle is broken: given the block (NFA) preventing common use, a loophole was found and exploited by the public to satiate the common demand. We can now subpoena the sales figures for an identifiable specialized product (braces), fairly estimate that only a tiny fraction of those sold were for the “intended purpose” (handicap use), and reasonably conclude that upwards of ~1% of total population acquired it for a singular purpose: constructing what is, for all practical purposes, a short barreled rifle - in quantities that must be considered “common use”.
Your posts here seem to ignore several facts. First, pistol braces did not come into common use simply because "the public" found and exploited "a loophole" - the federal government was an active participant in the process. ATF provided written pre-approval for the manufacture and sale of pistol braces, which clearly differentiated between the braces and shoulder stocks.
Second, neither floppy pieces of foam with nylon straps, nor thin pieces of rigid plastic shaped like knife or axe blades, can be reasonably construed to be shoulder stocks - even if they might resemble such stocks from particular angles of view. That is exactly why ATF approved the accessories in the first place.
Finally, you assume that those who purchase braces do so with "a singular purpose: constructing... a short barreled rifle". Obviously, there is no way for you to substantiate that claim; and it could be said with equal fairness that pistols equipped with braces were purchased or constructed because many owners desired 'a long barreled pistol', that could be more safely & precisely controlled via use of a brace. Frankly, the overall tenor of your posts here reminds me of material from Giffords or Handgun Control Inc, or possibly some ATF bureaucrat trying to rationalize that agency's attempted 180 degree turn on the legality of pistol braces...
That works for me! I suppose bump stocks are another example of trying to get around the circular argument. Which is not to say that the gun grabbers, and, especially those in the F-troop, aren’t trying to exploit the circular argument articulated here.