Private Road transport users do not pay a fair price. The massive externalities of private car use (environmental, pollution, road trauma, health costs etc.) are NOT borne by the private car user.

I agree with the first of those sentences. Private transport users pay way more than a fair price, in order to provide tax revenue to other parts of the community, including public transport. Road trauma and health costs ARE borne by the road users, both in terms of the actual effects of the events, as well as massive insurance costs. We get roughly 100% taxation on petrol, large rego charges and ever increasing numbers of taxation cameras on top of that.