That's why I said earlier that if they toll the road it should be for all road users, not just those that want to pay. That's how it works for all other forms of transit. If you fly, take a train, the subway, rent a car, etc then everyone pays. Sure, there are people that can pay more for a 'premium' ticket, but everyone still pays.
You know all those condo and commercial towers inside the downtown core pay taxes that go to the city right?
So I use the public road when I bike; by your all-users-are-equal scenario, I should never ever be confined to a piddling single-file bike lane, that's routinely obstructed by construction, deliveries and short and long term parking. Nor should I politely move to the side to accommodate drivers who could go faster than I can when there is no 'special' lane for me.
Everyone does pay for the roads, that's why they're 'free'. But just because I paid for the sidewalk, I can't pull my car onto it to park and avoid the ticket I'd get for prohibited parking on the road. In fact I'd get a bigger ticket. And if I want/need to occupy a traffic-lane I apply and pay for a Lane Occupancy Permit. Specialized facilities and tailored treatment are just one of the many ways we all get our share of the goods and services we all pay for.
That road's still free and still there for all, but like buying your way into a clean, filtered pool, or into a Green P lot, if you want the extra convenience, you pay extra.