I wonder if sth. like an electric Vespa would be feasible. You would be able to pack in more battery than an e-bike, but the last mile would be a problem because you can't just pedal the rest of the way.
Not only it's feasible, it's done. Cf. Gogoro for the most iconic ones (but there are plenty of other brands too).
The problem in Singapore is you need to get a COE for motorbikes. They cost at least 5x what am ebike would cost. I want an electrical assist bicycle that goes 50kmh and is nimble not a scooter that goes 80kmh, costs an order of magnitude more and rides like a death trap. I'd be happy if they provided some sort of intermediate license with a test for faster ebikes.