They have already done something like this in some states in Australia. The respective governments consulted with interested groups who may have been effected (surpirse, surprise) and came up with a proposal.
What resulted was that swords and knives became restricted
weapons. Meaning they didn't need to be licensed but if you were found to be carrying any you had to prove that you were part of an exempted group (martial artist, medieval re-enactor, fencer etc.) and that you had a legitimate reason for carrying it e.g. going to training or off to a medieval event or such.
This came about for much the same reason, escalating number of assaults and home invasions where the assailants were brandishing knives or swords.
Of course you could just get youself one of these Bedside Tables
if you're worried about home invasions