I'd keep them long enough anyway to cover any waiting periods of any sort if you switch insurers, had an incident last year where got a call day before a childs procedure to say it wasn't covered as he wasn't continually insured which he had been since birth but with several companies. With all the mergers/takeovers in the health ins industry there was not a seamless continuous record of cover due to not all records apparently transferring over from one of the taken over companies to their new owner.
Spent ages on the phone trying to chase it up but luckily had in my files a few actual letters from the company in question which gave the policy number so was able to get Company A to send email to Company B confirming cover, it was a right mess the evening before morning surgery!
I had been trying to cut down on retained paperwork as I'm a great hoarder of household records of all sorts but this certainly didn't help! Didn't give me great faith in paperless records either.