Much of the on-street parking is paid parking. If you're proposing that these scooter companies pay per hour that each scooter is left on the sidewalk, I think that's a great idea.
Really, I think its probably only a small fraction. Most residential neighborhoods have free parking, even many commercial areas. Do we have stats on this to be sure?
Parking, even in “free” residential areas is time or permit restricted. So even if payment is not direct there are other indirect payments and constraints.
Not left on the sidewalk, the scooter should be left on the street - a dozen scooters in the space formerly occupied by one car. And they should absolutely pay to use that space! Residential permits in SF are $150/yr. 50c/day per spot. Less than 5c per day per scooter. I think scooter and bike share companies would eat this opportunity up