Especially, mobile devices like laptops, smartphones etc will then have to send probe requests constantly, even if youre away from home... informing any eavesdropper around of essid and probably also bssid.

Most OSes do this anyway to speed up the connection process (try to attach to last n networks and see what sticks). Can be abused to learn about past locations of that device by asking one of the wifi location api databases (iOS, win, google/android):

https://www.mylnikov.org/archives/1170

Edit: couldnt find good links about rapid wifi connecting procedures but here's an older article about Apple's rapid dhcp mechanism:

https://cafbit.com/post/rapid_dhcp_or_how_do/