Doesn't work in France with its huge number of toll roads, and in the UK where fuel duty is the largest single part of the price of fuel, it more than covers the cost of public roads, yet people still drive everywhere in increasingly large vehicles. It's not gonna reduce driving, though I do agree it should not be subsidized.
The reason why British people are able to afford large and expensive vehicles is the heavy reliance on credit. 84% of new cars were bought on finance in 2024[1]
[1] https://assets.publishing.service.gov.uk/media/6781339100e3d...
Road damage is exponential with weight, so heavy vehicles are still heavily subsidized in France even if the total revenue is correct.
There was an interesting court case where only giving tolls to 18 wheeler was problematic but the equivalent fee for cars would have literally worked out to under 1 cent.
Public transport (especially trains) is very expensive in the UK. If you already have a car it's cheaper to use car even if you're traveling alone. For two it will be more than 2x cheaper than a train. If trains will be affordable I'm sure more people would use them. As to the size - during relatively good pre-COVID times SUV become popular but not many Brits can afford large vehicles today and on average cars in the UK are much smaller than in the US, I would not say it's a big problem.