There won't be any need to disable the radio for unused bands. Powering down unused hardware is literally the first thing the engineers do to save battery life.

Edit: can't reply due to rate-limiting, but in principle, all they have to do to search for service is power up the receiver briefly, running at a very low duty cycle. This has no noticeable impact on battery life or any other aspect of the phone's operation.

But why would the hardware power down if it is constantly searching for a 5G base station, not find one because of OPs location?

Mobile networks have more management functions than WiFi, for instance.

If you're in a high density area, the mobile network will push the device to small range cells (handover), or tell the device which other cells are available in that area (list of neighbor cells).

However, the smartphone is not required to search for a base station all the time. It receives hints from the network.

From practical experience, it’s very common for people to find their phone (iPhone or other) burning through tons of battery when they go out in the sticks, and this is reliably fixed by turning off cellular data. So either it’s not as easy as you say, or they haven’t bothered solving the problem.

If there's no service at all, that may be a different matter entirely. As ndjskska says, the cell network itself keeps the phone up to date with the nearby topology, so there's no need for it to keep pinging for a service that isn't there.

iPhones can limit between 4G, 3G, 2G for quite a while now, I'd assume this option would continue on.

60 GHz (802.11ad/802.11ay) is better suites for AR/VR, is already out, and doesn't have interference issues due to physics.

6 GHz should be focusing on devices that need to work at range not ones that can already be served via in-room frequencies.

Would 60Ghz (300-500m for 802.11ay) be competitive in power consumption with VLP 6Ghz (3m)?

Setting the data rate and transmit power to the same power sure, there isn't anything particular special about 60 GHz compared to 6 GHz other than 60 isn't going to make it through drywall.

Qualcomm has actually been releasing phone chipsets with 802.11ad for a while now. Intel did it for wireless laptop docking. Qualcomm's 5G modem also comes with 802.11ay but I don't know of anybody else that has deployed it yet.