Beijing (one example) has bike sharing without stations. Just dump the bike wherever and the bike sharing guys will deal with it. This is an interesting data point, because it removes the infrastructure bottleneck entirely (but makes a mess). What we learn from it is that bike sharing is bottlenecked and that it can grow a lot by widening that bottleneck, by adding more "stations."

European cities ( early to the bike sharing game) are really unlikely to allow such mess. Scooters may be another way of achieving the same thing, because they can be extremely space saving.

In my European city (Dublin) bike stations usually take up about 4-6 parallel parking spaces and a little bit of road and sidewalk. We don't have enough of them because that amount is space is hard to come by. I think a scooter sharing station could half or quarter the required space, with the same footprint. .. especially folding scooters.

At a pinch, I think you could get a station onto a single parking space. This makes finding room for them way easier. This means we can have more of them, maybe much more.

As to the benefit of powered scooters: cheap, small, fun, carriable, effective over short distances. Cons: need power, not as fast/stable as a bike and less suitable for longer journeys.

I doubt any of these are as important as the availablility of stations near where you want to start and end your trip. I think scooters>bikes in terms of space, and space is the right problem to solve.