The problem isn't about 'rapid release cycles', but about the UX design of the update process. Even before the rapid release cycles, Firefox would check for add-on updates every time it was started. Chrome's update mechanism is completely seamless and invisible and requires zero user attention.
Which, ironically, is almost as bad, when you suddenly realize that you basically let Chrome change the UI, and there's no way to return to the UI you once knew.
Except that Chrome has never really changed it's UI. The presentation at the end of Google's 2012 IO Day 2 keynote actually timelapses through the UI. The only change is the removal of the home button outside of general micro-tweaks.
