It has proven to be a disincentive in every jurisdiction in which licensing of cyclists has been trialed, has cost more to implement and administer than it's taken in and only left motorists more frustrated with extra traffic volumes. If traffic keeps going the way it is in Dublin, I might have to start cycling my commute.
It certainly did increase the price of bikes here, though not massively as you suggest, but most if not all costs to the state have been recouped through additional employment, tax on significantly increased sales of accessories, clothing and servicing. It's predicted that the increased activity levels will also save the health service money over the longer term, but that's harder to put numbers on.
Every tax payer contributes towards those costs, there is no special fund that motorists pay into, so that argument is moot. I don't have kids, yet my tax goes to pay for their schools, their free GP care, etc., I've never been unemployed, but my taxes also contribute towards those who are. I've always paid my own way in terms of accommodation, but again my taxes those in receipt of state aid. That's just how the tax system works, you don't get to pick and choose.
So to introduce equal treatment just for users of the various transport methods, as our motor tax system is emissions based, cyclists would pay zero, or such a token amount that the regulation and administration costs would far exceed the revenue taken in. It could even be argued that bikes have such a positive impact on the environment that cyclists should be incentivised. In fact, incentives are already in use or being trialed in other countries as a means of addressing worsening urban pollution due to the increasing populatiry of small diesel engines. France pay cyclists 25c per km cycled on their commutes following a successful 6 months trial there resulted in fewer cars on the road. Zero emmissions cars also get a €5,000 credit from the taxpayer here. Perhaps we should offer a level playing field there and extend similar credits to bikes? Extending the logic of funding road infrastructure only by those using it, those taking trains or buses should surely pay a lot more as overall, those are heavily state subsidised.