250 Watts will assist a rider perfectly fine on flat terrains, but is woefully lacking on steep inclines. 500W I would say is minimum to aid a rider to climb a steep hill without going into lung busting exertion. We are talking about casual riders who use their bikes infrequently.
500W? Minimum? Seriously?
This is in excess of what any cyclist except maybe elite ones can maintain for more than a very short time. How long will vary but everyone will be in the red and won't be able to hold it.
If 500W is the
minimum assistance needed, and 250W is inadequate then the only conclusion is that humans can't climb hills on bikes.
When I rode the Tourmalet (1,600m at 7.4%) earlier this year my average power was 184W. So how on earth did I get to the top with such inadequate power? It should have been impossible. In actual fact power was never an issue, endurance over the last few 100m of ascent was the problem as my human "battery" ran down.
My peak, which I only held for a matter of seconds at a time was 450W. Still 50W short of the minimum continuous rated power of 500W that you propose.
With a 250W assist I could have "glass pedalled" all the way up, contributing nothing, and still got up OK.
Now the Tourmalet is a pretty gradual incline but on that Pyrenean holiday my wife (who never cycles apart from on holiday) could leave me for dead on more serious 10%+ inclines. She was riding a 250W EAPC mountain bike.
So in what world can 500W be considered as a
minimum assistance? Remember this is an
assistance, and the rider will be contributing.
What you're describing is a light motorbike, not an assisted pedal cycle.