YEP...I am well aware of UK laws on these little beasties...The governmental structures that you have over there bleed more British Pounds out of you folks than a blood bank restocking their supplies during a blood drive...lol...lol.
The bottom line is it's all about the money to keep supporting the cradle to grave, womb to the tomb, nanny state...lol.
Here in the State of New Mexico where I live, there are no regulations on motorised bikes, no registration, no insurance, we do not even need a drivers license...lol...They are just treated as bicycles here, just follow common sense rules of the road etc. and it's all good...We also have to have lights if riding at night as well as a horn or bell.
Chapter 18 – Other “Vehicles”
Section E. Motorized Bicycles
Revised November 30, 2017
Motorized Bicycles are not considered to be mopeds or motorcycles.
By current MVD practice, motorized bicycles are considered to be bicycles (not mopeds or motorcycles) and are not subject to the titling and registration requirements of the Motor Vehicle Code.
And we do not even have a helmet law if your under 18 years old...I don't ever advise that though, I always where one when riding.