For whatever it is worth, use of a front brake on ALL bicycles has been required in the U.K. since 1936 or so. In 2017 a British court cleared a brakeless fixed-gear rider of manslaughter for striking and killing a 44-year-old mother of two, but
he was convicted of causing bodily harm by "wanton and furious driving."
The brakeless fixed-gear fetish has long roots, back to the 19th Century, when early safety bike riders advocated the "flying dismount" as a means of stopping. Later, track riders on the streets would use track mitts with extra heavy palms, reaching UNDER the handlebar and using their forearms as fulcrums to brace against as they shoved the thickened palm the glove onto the tire, essentially creating a crude spoon brake - and those were history more than a century ago. The only U.S. cycling manual for adults from between the wars I can find advocated running a front brake on all fixed-gear bikes ridden on the public roadway.
The fact that we have no such regulation in the U.S. is more a relic of how bicycles have been relegated to "toy" status in this country.