Two-wheeled cargo bikes are already starting to get popular in my area (although I imagine plenty of people see them as an annoying hipster affectation). People ride them pretty carefully -- taking the entire lane, etc -- as they're often carrying children.
So, I'm not so sure electric rickshaws couldn't take off.
Yeah, I see a few cargo bikes round my area (Bristol) too.
I'm not sure what the licensing requirements would be for e-rickshaws in the UK, though. I imagine you'd need registration, MOT and insurance for a non-pedal vehicle and that would make cargo bikes far more economical. If we had pedal e-rickshaws, they'd likely be limited to the same power as e-bikes and only for assist which would make them less popular and I can't see manufacturers being interested in making them.
So, I'm not so sure electric rickshaws couldn't take off.