Why not use fwupd? (link is the Arch wiki but should be relevant for any distro). I've been using fwupd to keep my Dell XPS15 BIOS updated for the last few years, with no problems at all.
I'm not sure why Docker would be a particularly good (or particularly bad) fit for the scenario you're referring to.
If you're suggesting that Docker could make it easy to transfer a system onto a new SD card if one fails, then yes that's true ... to a degree. You'd still need to have taken a backup of the system BEFORE the card failed, and if you're making regular backups then to be honest it will make little difference if you've containerised the system or not, you'll still need to restore it onto a new SD card / clean OS. That might be a simpler process with a Docker app but it very much depends on which app and how it's been set up.