@gemlog
I think your first reaction was correct. If you have some people paying to get preferential treatment, and why else would they pay extra, everyone's focus will turn to the paid for service. Better to tax some more and deliver a better service for everyone.
Also, where would things stop? Semi-privatised education. How about semi-privatised police where the rich get crimes solved faster, for a small payment? "For only $41 per month, get preferential service when your house is on fire".