If you're serious about analysis then you could start by [reading this UK government report](https://assets.publishing.service.gov.uk/government/uploads/...) and it's references.
Or a study on the [danish cycling infrastructure investment](https://cyclingsolutions.info/cost-benefit-of-cycling-infras...)
> whether some kind of funding-by-the-users is possible (like happens for other vehicles: fuel duty, road tax, etc.)
Revenues from both go into the same general taxation pot, they're not reserved for funding roads. Incidentally, Tesla and other e-cars pay neither.
Any action they take will 'cost something', even not doing anything (lack of repairs will cost you double in the long run).
Don't worry about 'funding by the users'. Cycling is a net-positive for population health and government goals (exercise as well as less congestion and pollution); by that logic users should be paid for riding a bike! Besides, most cyclists pay taxes already; or are you advocating charging pedestrians for the use of pavements as well?