Underwriting profit hasn't always been a big component of insurer profits - typically "float" or that interest on the premiums held has been the big driver. But in a low interest rate world, companies have had to keep more and more underwriting profit in order to exceed cost of capital. As they need more UW profit, so the fight over claims gets worse...

You are right though that money needs to be set aside for bad years - in insurance we call it "reserving", and actually it is already accounted for before the 5-15%. It is stashed away in the loss ratio as "incurred but not reported" or is paid in reinsurance premiums, which are a fixed cost. 5-15% is what is left over after all that (and admin expenses).