Some thoughts, having practiced a bit on infrastructure law.
To a car owner all toll-stations seem alike but the legalities for each can be very different. Toll roads in India come in a few flavours:
(A)
Tolls collected by the Central / State government (i.e. they receive the money directly -- although the physical collection can be outsourced to a private operator) -- best example is Mumbai-Pune expressway
(B)
Tolls collected by a private contractor who has also developed (or modernised) the road -- best example is NH8 stretch from Delhi to Gurgaon where DGSCL (private company) modernised and were granted rights to collect toll.
The
risk / rewards of Tolled Roads of type A above are borne by the Central or State Governments directly (For Centre it is NHAI and for states it is State Infrastructure Boards or Department of Transport). In some cases they construct the road directly, in most cases they engage contractors like Gammon India, SEL, etc. who are pure contractors and are paid a fixed fee. In some cases the contractor also manages the tolling but bears
no liability if the toll collection is low (due to low usage).
In type B roads the contractor usually undertakes a traffic study before bidding so as not to get into road development where traffic is likely to reduce. In such cases they have a fixed obligation to either the state or central government (vis-a-vis quality of road, material used, etc.) but must recover their costs and make profit only from toll receipts.
In the private sector the type A roads are usually termed '
annuity' road projects (to reflect risk of not getting paid the lump sum by the Centre/State governmennt) and the type B roads are termed '
toll' projects (to reflect risk of not getting toll).
So using the permutations and combinations we could have
Central road -- Toll goes to Central Government (A)
State road -- Toll goes to State Government (A)
Central road -- Toll goes to Private operator appointed by Central Government (B)
State road -- Toll goes to Private operator appointed by State Government (B)
From my experience I have observed that the vast bulk of road projects in the country is Type A. Pure toll projects where it is in the interest of the toll-collector to increase traffic are few.
Now to move on to car taxes. Car taxes include both central taxes (excise) and state taxes (eg. road tax, octroi). These are collected together by the manufacturer / dealer but paid separately to respective governments.
Re the proposal that OP has mentioned, I could frame the following questions:
(1)
Is it possible (practical) to increase central / state taxes (or institute a central / state cess (i.e.tax) on new cars) and reduce the toll rates on (respective) central / state roads?
A: Yes, it is not difficult at all except that practically a central cess can reduce toll rates for central roads only and a state cess can reduce toll rates for state roads (within the collecting state). This is easiest for Type A roads. For Type B roads reduction in toll rates would require renegotiation of terms with the road developer which could become prolonged. However given how few type B roads there and the existing interest of the type B road developers in type A projects I do not believe that it would be very difficult.
(2)
Is is possible to increase central / state taxes (or institute a central / state cess (i.e.tax) on new cars) and reduce / eliminate toll rates on all roads?
A: Very unlikely given that this would not only depend on the state government reaching an understanding with the central government but also the fact that state governments will be reluctant to share state cess from cars sold in their states with other state governments (to offset reduction in toll in the other state). For it to work all states would have to agree that the aggregate of the state cess collected by them would be pooled into a single fund from which they would receive payouts proportionate to the length of tolled roads they have (bit like Finance Commission which apportions part of centrally collected taxes to states).
The most likely possibility is for the central government to reduce / eliminate toll on central A and B roads by levying a central cess.
(3) Is this idea desirable?
A: Well judging from the comments on this thread this is a hot potato among BHP-ians

All I can say is that there are millions of public utilities that we do not even know about let alone use for which we are being directly and indirectly taxed / cessed.
For eg. -- We pay an education cess with income tax but many of us (or our kids) do not go to government (or government-aided) schools. So we are cross-subsidizing someone else's education.
Or going by the budget 0.1 paise of every rupee you pay as income tax is used to modernise and renovate museums. How many of us regularly visit museums? Same is the case with development of railways or primary healthcare in rural areas. A well-to-do city dweller could argue that he gets zero benefit from utilisation of his tax rupees towards such utilities.
Or take the case of a few fractions of your tax rupees being used for opening an embassy in New York that 99 % of taxpayers will have no occasion to use or derive benefit from.
By the way, just for info there are similar laws already. Under the Central Road Fund Act, 2000 a cess is collected on sale of motor fuel to be used by the Central Government for development of roads (mostly national highways). Is that unfair on people who barely use NHs and mostly do city driving -- I guess it is. Point is that there is no end to uncovering 'public utilities' that you pay for but don't use.
My view is that if we had to ensure that tax money paid by a tax payer is used only to benefit utilities / services a-la-carte that he or she specifically uses or befits from it will be impossible to run a country.
I hope this helps form a view.