Why should there be an excess?

The insurer normally imposes some excess as this would serve as a form of co-insurance. With an excess, the insured would tend to be more careful because if a claims occur, the insured also has to be out of pocket and contribute towards the claim. In general, the higher the excess, the more careful would be the insured and hence the lower risk of having a claim, to reduce frivolous (unnecessary and avoidable) claims.