In principle I would pay more for a certificate to get better service, but only if the increase was directly linked to that increased performance.
So for instance. The certificate cost doubles. But if the duration between receipt of the paperwork and issuance of the certificate takes longer than 3 months, half the cost is refunded. If it takes longer than 6 months, the entire cost is waived.
That might be some slight incentive for the police to actually work towards efficiency, whereas right now, they get the same fee no matter how crap the service is, so why would they bother to improve it?