OP is not complaining about how much the tax covers, but who (people who drive and who don't) pays what percentage.

> we subsidize private transport (our taxes pay for the roads, traffic police, etc.)

My point is: this "we" includes all those drivers too. That is, whatever the $$ that gets paid into maintaining the infra, it comes from "we", which include the drivers. And since the non-drivers also need private companies/drivers to move things around, they are also part of the story. They do not subsidize anything.