Mike
Couple of comments. First, thanks for the reasoned response. This topic all too often degenerates into "If you can't afford 91 you shouldn't be driving a BMW" or something similar. I think the engineering and science is actually interesting here.
You say that the car "detects you are running 87" but I don't think that is the right way of saying it. The engine has no way of knowing specifically what you are running. What it can determine is that there is persistent knock being experienced, which could be caused by lower AKI, or higher temperatures, or altitude, etc, or a combination of the above. Since AKI is determined by comparing a fuel to a reference fuel on a test engine, a very artificial environment, and since different fuels of the same AKI can vary in their knock responses at low rpm vs high rpm, at full throttle vs partial throttle, etc, AKI or octane rating is not absolute. I agree that persistent knock can push the DME into a different map, but it is because of the sensors hearing the onset of knock, not because of the fuel in and of itself.
I understand your point that shifting between maps can come with a lag, probably due to time-based averaging, but I can only comment that I haven't heard pinging due to that issue. Even if there is a lag switching to an alternate map, that wouldn't cause the knock sensors to stop working. It may cause the engine to use a less than ideal map in terms of efficiency while the DME adapts.
You also say "BMW has recommended 91 as a minimum because they know that anything less will cause knock in unfavorable conditions". I don't agree with that, because AKI or octane rating is not an absolute. In the real world, assume that fuel qualities overlaid on varied engine conditions will result in the onset of knock according to a bell curve or Gaussian distribution, ie lots of engines will experience the onset of knock at a typical AKI, fewer will experience it at a lower AKI, and fewer will experience it at a higher AKI. It is no good designing the engine to run precisely on 91, because in that situation, half of the population would have knock (all the ones on the right side of the bell curve). If BMW wanted to make sure that no owner ever had knock, they would specify a fuel way over to the right side of the curve, so that all (or nearly all) were 'safe'. But that would mean that most owners were paying for fuel they didn't need to pay for, ie cost without benefit. So they pick a spot a little over to the right, good for most owners most of the time, and that turns out to be 91 AKI. The engine is actually designed to run on something less than that, ie the mean or peak of the bell curve, recognizing that there are a range of fuels sold as 91, and a range of operating conditions.
So, some may have problems on 91 despite the best intentions of all involved. Many will run on 91 forever, with no problems, and no need to think about it beyond choosing the 91 nozzle when they fill up. But some of us checked our local fuel, and found that the engine ran every bit as well on 89 (my example) or 87 (others). They aren't wrong, they are just fortunate to have a combination of local conditions, fuel quality, and engine condition that works fine on that AKI octane rating. My engine was new when I ran it on 89, and it may be that at high miles, it would have required a higher AKI.
Finally, in my experience, soccer moms can experience pinging at least as often as other drivers, due to the use of a light foot on the throttle on a long grade.
Jeff