PaulDavis battery drainage, and being tracked when out shopping etc are immediate thoughts
I think for many users battery life depends more on which apps are running and using the network than on power usage by Wi-Fi while not connected. I can get multiple days on a full charge.
While out and about,the GrapheneOS Wi-Fi setup, which does aggressive MAC-address randomization, among other things (see: Wi-Fi privacy), is not believed to be a noteworthy tracking risk. The sole exception would be if a device is aware of one or more so-called "hidden" Wi-Fi networks, which force the device to continuously leak information about those networks ("hidden" Wi-Fi networks are a privacy risk and, if used, should probably be deleted from the device immediately after use -- see, for example, "Hidden Network" on this Apple page explaining why their devices warn users about "hidden" Wi-Fi networks).