And they didn't.....

John Wood in his book "An Essay Towards a Description of Bath(1749) writes that the wearing of swords was forbidden by Beau Nash after fights broke out between gentlemen and the chairmen of Bath, who were known to be rather belligerent by nature (and presumably were also very strong fellows).

Gentlemen who had been provoked by the insolence of these chairmen, the gentlemen would raw their swords on them and the chairmen would then defend themselves using their poles. (See Volume II pages 411-12.)

Oliver Goldsmith wrote about this in his Life of Beau Nash, and gives the reason as a duel fought in the streets of Bath where one man died: he also thought that Nash banned the wearing of swords because they often frightened ladies and tore their clothes (Volume III page 305).

It’s interesting to note that the Bath Chairmen wore a distinctive uniform.