I got a very different impression of this method than you did because I saw it as, just as with an A/B test, when you make a major change to the site, you reset your counters. This makes your point #2 mute. As for number 5, why couldn't you use the same cohort analysis with this method?
moot == "of little or no practical value or meaning; purely academic."
moot/mute is a tricky word combo because smart people can justify using "MUTE" instead of moot, and english is such a terrible language w.r.t. spelling there are no good clues to use one versus the other (and "moot" is far less commonly used).
Off-topic: Most of the time, such grammar/spelling corrections get downvoted because people think they are nitpicking and don't add anything to the conversation, or are rude somehow, but as a non-English, I appreciate them a lot!
I've seen minor tweaks to a form raise conversions by 20%. The person running a particular test may not even know that a particular change was significant, or even that it happened. The change could be as subtle as another running test realized that version x is better, interfering with existing tests.
As for #5, with an A/B test you run into these situations, you're able to break down and crunch the numbers in multiple ways, and then have a discussion about how you want to proceed. But with a multi-armed bandit approach whatever complexities you have not thought of and baked into your approach, are not going to be noticed.
