Hopefully manufacturers update to just make sure all of these wireless systems fail to 100% on so that this is a moot point, but. . . .
That is an interesting problem to think over. Over the last year or two I've replaced almost all of the lighting in my house with Philps Hue bulbs, and all of them are controlled by battery operated switches in the form of either a battery operated Zigbee switch, or a zigbee Hue Switch Module wired to a mechanical toggle or push-button switch. There is no feature I'm aware of in the Hue app that turns the lights on when the switch battery dies. I believe it will alert you to a low battery though.
Everything in my house is integrated to work together using Home Assistant, and I can monitor switch battery levels in that software, which means I should be able to write an automation that switches the lights on when the battery drops below a defined threshold. But imagine being asleep at 3am and all the lights come on.
A project I've been thinking about recently is to move all of the Hue switch modules to a central location instead of buried in the switch box as my wife and I have been discussing a plan to sell our house in 5 years after our daughter graduates; I don't want to rip all this stuff out, and having it centrally located where someone can easily work on it in the future would be nice. I just looked online out of curiosity, and I see there are CR2032 battery eliminator kits that replace it with a hardwired disk fitting in the battery slot and connecting to either a wall-wart or USB power source. Now that I know that exists, that's exactly what I'm going to use.