The car was not designed to run on runflats. It was a space saving option and the suspension has not been compensated for runflats.
To the OP....... I too ran my last few MINIS on normal tyres with no issues. However, I got the option to have a pair of cheap runflats to try. I had a puncture a week later and it got me 50 miles to work . If I did not haver the rf tyres on, I would have had to rely on the rubbish tyre weld that they supply to get me to work. Since being spooked, I now have run flats fitted on both MINIS. Yes, the ride can be crashy, harsh but id depends it you want to be potentially stranded. I drive in Europe and would not want be stranded on the Stelvio Pass
I put up with the ride but will agree, the car is transformed when running non run flat tyres. Changing the tyres will no damage or have any adverse effects to your car.
With regards to the price you were quoted, I have just had Bridgestone RF tyres fitted to my Cooper D and paid £120 each. I usually pay the same price for Continental Sport Contact 3