Putting it on fuel would have some effects, whether that is good or bad would depend highly on your own circumstances (I would say) and your leanings on various issues -
Every high mileage driver I know of does the vast majority for business purposes. This will not go away if VED was put onto fuel. BUT as the highest mileage drivers they would suck up a disproportionate amount of the total tax take, either reducing profitability of businesses or passing the cost onto consumers, thats the nature of any factor that increases costs to a business. (our businesses often complain they are treated harsher than foreign competitors this just exacerbates.)
VED is a simple and effective way of encouraging the less feul efficient vehicles off the road. I am not talking the odd M3 tucked away and used for 2000 miles a year but things like high mileage mondeos used as regular vehicales. People suck up the fuel cost but they complain like hell when they have to fork out a significant chunk of cash in one go for VED. Plenty of people have no idea what MPG they actually get, they complain about the cost of fuel but make far more fuss when its time to tax, so it clearly makes them think.
Due to the amount of tax on fuel there are already people using red, chip fat (without paying the duty), using knocked off fuel etc. The bigger the amount of tax per litre the more benefit construed by avoiding that tax.
Fuel theft will likely go up as the fuel becomes more and more valuable.
Demand for fuel is VERY inelastic, it really changes little with price rises, I could envisage more people feeling better off after getting rid of £240 a year road tax yet paying £5 a week more on fuel since many people are incapable of relating simple maths to money.
Its a tax. Tax is mostly illogical to most people, lets not start assuming tax is going to be made logical. Logic and tax go in the eye of the beholder, its only logical if it suits your views.
I think I have heard just as many people remark about low/no VED as I have heard make a fuss about MPG. The two are intrinsicly linked obviously but I don't think a lot of the general public actually "get it"
The raw value from VED is fairly predictable and can be modelled on customer vehicle selection trends and expected life on the road. If you moved it to petrol/diesel its a different matter, as vehicle fuel efficiency improved the rate would have to go up to maintain the same tax take. Assuming the government had a "target" tax take then as efficiency went up or as they decided they needed more money from this extra fuel duty tax they would have to change the rate increasingly upwards. It may be 30p per litre in 2014, and 40p a litre in 2015. Why? because suddenly a new super diesel improved diesel efficiency by 25% for all diesel cars, this had to be offset by a higher tax so all petrol fuel users would be significantly worse off from this effect in order to balance the tax take.