They do that already... sum of all privacy losses.
Any time you go out in public your devices are crying out looking for your home AP. If someone can figure out which are you, e.g. by seeing you multiple times in different places they can then go look up where you live based on your home's SSID broadcasts.
Correcting myself: It appears that many modern client devices (at least current Networkmanager in linux, iphones, and grapheneos) have a "hidden" flag on saved SSIDs and only probe for hidden ones, so the ancestor post is correct for a least these devices.
Older and less sophicated clients, -- that don't explicitly have a 'hidden flag' for saved SSIDs will probe continually for all SSIDs they know.