Joseph,
“And last time I checked, i don’t recall women to follow that rule at all… Even the Brisker’s allow the women to carry in Jerusalem…”
GAON: Why are you differentiating men and women regarding this Halacha? And which “rule” don’t women follow?”
Rule = “Baal Hanefesh” leHachmir.
“Why are you differentiating” – I’m just stating a fact. All Briker Ravs kids permitted/ed their wives to carry in Jerusalem – that is a fact.
Now why?
“Baal Hanefesh” leHachmir’ is not for anyone to claim so, if you learn through the inyan and determine from that there are shitos leHachmir, then you can say you want to be machmir, otherwise you should just follow basic halacha and the minhag.
Yes, I know nowadays each and every Am Haaretz proclaim themselves as a Ba’al Nefesh’.
However – ask most of these Anti-Eruv hotheads which Siman in Shulcchan Aruch you can find these particular Halachas? and they won’t even know to answer…