"the electric motor shouldn’t be able to propel the bike when it’s travelling more than 15mph"
Curious now whether that's actually what the law says, if so it seems badly drafted. That would appear to mean a physical limit on the motor is required rather than just a software control - as then the motor would "be able" to propel the bike faster but he device as a whole, unmodified, would not.
That's pretty fast for a commuter IMO. In heavy city traffic 15mph is probably above the average for cars? [quick check on Google, single search, only gave me that [some?] Melbourne rush hour traffic averaged below 20km/h (~13mi/h)].
TBH 15mi/h seems about right for an all ages accessible motorised bicycle.
With some of the long backups you get at lights around the belt in Houston (the lights are far apart, weirdly spaced, the timing is a nightmare, I'm sure), I get around 18 mph if I coast between stopped cars on divided highways and about half that if I drive like a car.
I obey the other laws, even signaling and all, but I'm almost positive lane splitting like that is illegal on bicycles (I know it is for motorcycles).
The drivers are also much worse the further out you get, since there aren't bike lanes or sidewalks (illegal but better than getting harassed), and people don't seem to know you're allowed to own your lane. My commute is mostly in a manufacturing area, with lots of dump trucks and 18-wheelers. I've been yelled at and pushed off the road by angry trucks and trailers several times.
Having something like this to get me up to the flow of traffic quickly would keep people from having to go around as much maybe, but I'd rather get one of the small gasoline engines and tanks for about half the price.
https://www.gov.uk/electric-bike-rules
(Otherwise it'll be a powered two-wheeler, come under moped regulations, require a license, license plate, etc.)