But that only works if scooters are ubiquitous enough that you can find one when you want one.
If I have to walk 5-10 min to the nearest car which I can unlock from my phone and then use to drive 5 miles somewhere then it's great, but if I have to walk 5-10 minutes to the nearest scooter pickup so I can scooter somewhere for 5-10 minutes then it sort of defeats the whole point.
As you said, if it's much longer than that, then there's no point -- I don't think I'd want to ride a scooter more than a mile or so anyway, so if it takes me 10 minutes to find one, I may as well just walk the whole way.
If it's getting later in the day most of the scooters you find are going to be scattered in all sorts of very strange areas, many times in gated apartments, and/or with not enough charge to get you home. Or maybe you have to settle for that scooter with the screen dangling out of it by the wires and the handlebars at 45* relative to the wheel that everyone else was just not desperate enough to use.
This is certainly true for the hire bikes in London (scooters don't seem to have gotten permission for many areas yet).
One of the biggest detractors is that you could ride a scooter to work and when you go to leave, realize the nearest scooter is half a mile away.
Assuming the following:
Cost to buy: $500
Cost to charge $0.40/day (maybe generous)
Cost to Rent: $2/day
Rental Mileage: $0.15/min
Assume 10mph average, (10 miles/day) $9/day
Total: $11/day to rent
2x/week,50 weeks
100 days (200 rides):
Buy: $540
Rent: $1100
No way it’s economical to rent scooters routinely. Even if you break your scooter every 6 months, you can still save by buying a new one.
And who wants to ride scooters you know are abused? Heck, I rode one and the brakes didn’t work.