An increasing number of cyclists do have insurance, those who belong to cycling clubs. The problem (and it is a small one as there are few 'hit and run' cyclists where compensation would be appropriate) is one with casual cyclists (like you for example) and bad cyclists who don't take it seriously.

But if you are cycling occasionally and believe that all cyclists should get insurance, then I would suggest that you first check your car insurance or home contents insurance to see if it covers you for 3rd party costs while cycling. If not, you might want to buy such insurance, just like the most serious cyclists do.

If you think this is something that should be compulsory or is needed to protect pedestrians, then I hope that as an occasional cyclists you will ensure that you are adequately insured.