The original post by the original poster is absolutely correct. I say this as a responsible cyclist.
Insurance, the best that there is, is provided especially to cyclists and to all road users by:
https://www.eta.co.uk/
The insurance can be set up entirely online, and is quick and easy to do. Making a claim is also quick and easy to carry out. From memory, I pay £30 a year.
Any cyclist who doesn't have insurance is a total fool.
I absolutely agree about cyclists who ride on the pavements, and who carry too many items so that the cycle is unbalanced or they are not in control of the cycle. That's why I have a wire cage on the rear luggage carrier of my cycle, which carries two carrier bags of shopping. It cost £12. For heavier loads up to 50 kilogrammes, I have a trailer which is the same width as the handlebars of the cycle. It cost £120, is now three years old and has successfully made hundreds of trips.
If there is a tax for cyclists then fine. Number plates - fine - will help with cycle thefts.
The original poster, in her list, forgot protective clothing. Every cyclist should wear high-visibility protective clothing and a helmet. We all know, after seeing the TED talk about concussion in rugby players, boxers, and cyclists, that helmets don't currently protect against concussion - but the safety organisations are working on it. Helmets do protect against skull fractures. Four years ago, I was thrown from my cycle when going over ice. My head hit the road, and my jaw slammed shut, causing me to lose a tooth. Without the helmet, I would have been dead.
So everything that the original poster is absolutely correct. As more people give up motor vehicles and turn to cycles, then there needs to be good enforcement - and extension to - sensible rules.
One last observation. In the eyes of the police, a cycle is a road vehicle. It is not a toy, or exempt from traffic rules. The cycle has to be used properly in respect to the rules of the road.