While I am not against more bullpups being produced, they have been around for a very long time and they have not really been welcomed by the US gun community...which is probably the reason why you don't see more of them around. People just didn't like them.
While there probably were a few earlier, there were some custom gunsmiths in the 30s who built "bullpup" rifles. These were varmint guns (often in wildcat chamberings) built on bolt and some single shot actions. The advantage was getting a longer barrel in a gun of standard (or less) length, giving higher velocity and all that goes with it. Downsides were poor balance (not a concern to the varmint hunter) and the long trigger linkage needed made a really good trigger pull difficult to achieve.
Modern military bullpups essentially began with the British EM1 and EM2 rifles they developed right after WWII. Since then, there have been several other designs, some successful, (to a point) like the AUG, and others not so much.
They weren't really an 'answer' to the pistol brace issue before pistol braces were legalized and I don't think anything has really changed technologically that would see them as being welcomed anew.
This is a matter that should be discussed with precision. Specifically "braced pistols". Pistol braces have always been legal. STOCKED pistols became regulated by the NFA 1934. There is a difference. Its a matter of technical language, and legal splitting of hairs, but there is a difference and it matters under the law. We're currently waiting for the ATF to redefine what it previously defined, (with little hope for anything good for us), but under existing interpretation of the law, if its not designed to go against your shoulder, then its not a stock. And, if its not a stock, its not regulated under the NFA 34.
Until the ATF changes that interpretation (as it is expected they will soon) it doesn't matter how people USE the brace, its not a stock.
There are or have been braces for pistols for a long time, that weren't stocks, and some that acted like stocks, but were not attached to the gun, and the ATF not only allowed, but essentially ignored them. With the AR pistols, and, thanks to some foolish people on the internet, the ATF isn't ignoring them anymore...