Yeah, even cheap microcontrollers nowadays with support for clock functionality have an ultra low power mode were the only thing running is the clock crystal and the clock functionality which uses so little power that it can run for years from such a button battery.

The thing could do the same as my stupidly cheap alarm clock that has some batteries as power backup and just keep on counting time without displaying whilst mains power is down so that when mains power comes back up it still has the right time.

The extra $1 for the hardware needed for it is hardly going to matter next to the overal cost of anything but a stupidly cheap microwave.

Eh that’d be horrible. 30 min power outage and your clock is off enough to really throw you off.