Like everyone else I'm not a fan of the harsh ride I get from my run-flats but recently I have had some first hand experience with their advantages.
The first instace was when I came out to a flat tire and was able to drive to a gas station without worrying about anything. I drove like usual, added air and went on my way till I was able to get it plugged, very convenient.
The second instance is more financial and safety oriented, I hit a serious pothole and now have a nice bubble in the sidewall of my front left snowtire. Normally when this happens I get a new tire and inevitably waste lots of the tires treadlife and pay over $200, now I plan or riding it out till the tire needs replacing or it punctures.