£10 a year would be uneconomic. This is why things like dog licences were scrapped.
The economic arguments for not charging cyclists are that: they are generally healthier and thus require less maintenance for chronic conditions like obesity; they disproportionately reduce traffic, ie. the more of them you have the less you have to spend on roads.
E-bikes have the opportunity to dramatically increase the use of bikes for commuting and they also offer great economic benefits because they're expensive to buy and require regular maintenance, ie. more bike shops with skilled employees. But for this to succeed will require significant investment in road planning and safety. Note that anytime someone starts talking about helmets they're trying to avoid difficult questions about planning for road safety.