The bike only ever goes 20+mph on busy main roads to keep up with traffic where the only person at risk is me...
Did you miss my quote about the two cyclists who were jailed? Why did they get jailed?
People walked out in front of them while they were cycling on the road. Not on e-bikes either.
Unless you are riding on an empty road, with no other human or animal close enough to come into contact with you, thinking you are the only person "at risk" is a mistake. How will you stop yourself riding into a child that runs out into the road immediately in front of you. (Happens all the time.) Cars/vans/cyclists pulling out in front of you at junctions? Cars cutting you up as they turn across you, thinking you are riding at 8mph not 20mph? I'm happy to accept you are the best rider/driver on the planet. However, when you ride on the road, you are amongst people that aren't. In fact I would suggest most of them are barely aware of other traffic around them.
I'm not your mother, so you are free to ignore this advice. A 20mph
powered vehicle in the eyes of the law, makes you a
motorised vehicle. Without the same insurance cover, license, MOT that other motorised vehicles need to be on the road, you will be in deep do-do if you are in an accident where someone other than you gets injured. You think a court is going to be sympathetic when you say were riding an illegal motorised bicycle because it was cheaper than buying a motorbike for your journey? I can assure you, the courts (at the insistence of the Home Office) will give you the highest possible sentence the guidelines allow.
If you own property, that will be used for compensation and legal costs for the person you rode into, even if they ran in front of you. It's hard to get or keep a
good job with a criminal record. It's IMPOSSIBLE for you to be in the right, if your vehicle does not meet standards dictated by our laws.
While you may consider riding an illegal bike 'a bit of fun', people who play with fire, often get burned.
I don't know if it's any different where you are, but here in leafy Hertfordshire the police don't consider powered bicycles an issue big enough to spend time investigating. But after an accident that involves an ambulance being called to the scene, you can be sure an illegal bike will be considered the same as an illegal car/car driver, except your bike will not be seen by you again.
As to (cycling) club insurance, if the club members insurance doesn't include named club members, likely anyone riding under the club banner will need third party liability insurance to ensure the club doesn't itself become liable for any mishaps by its members.