I think most of the problem
I think most of the problem with all of this is the failure of the manufacturers to supply a spare tire of any kind, even a "doughnut". (With most new models, BMW doesn't supply anything. Perhaps this is to cut costs or trunk size, or to try to cut weight in order to meet fuel efficiency requirements. Whatever the reason, it is short-sighted.) With a spare, road service (free for 4 years with a new BMW, or, later on, well under $100 per year for AAA) will then be able to replace a failed tire with the spare, so that no owner will have to lie on his back in the rain on a busy freeway.
But I also think that, even with run-flats and no spare, no owner should have to lose the use of his car for several days while waiting for a replacement run-flat to be ordered and delivered. That is, some cheap non-run-flat tire of the right size will pretty much always be available to be purchased and installed immediately, and that tire can serve as a temporary spare until the exact run-flat match shows up. Again, it is an annoying extra $100 cost, but cheaper and better than being without the use of your car.
But, if a spare of any sort came with the car (or if the trunk were big enough to hold your own), then I imagine the best solution for most ordinary people would be run-flats (of the newer variety) with a run-flat spare. That would allow some possible further driving after a tire failure, and an immediate exact swap. For substantially less money, equipping cars with non-run-flats and a matching spare would solve almost all of the same problems (and allow performance aficionados a wider choice of tires and their concomitant benefits).
But the real villains in the story remains the manufacturers, who saw the invention of the run-flat tire as an invitation to eliminate the spare tire altogether, and a stop-gap solution to their size-weight-fuel problems. Run-flats do have some benefits, but, in any case, let's bring back the spare tire.