Yes, but the costs might prove to be too high. For example, if people owned their own, they wouldn't need people driving around town collecting scooters to recharge, and then driving them back to a drop-off point. Likewise, rented scooters probably have a far shorter lifetime due to theft, harsh treatment, abandonment and so on.
Yet electric scooters existed before these services started, and there was no major uptake of their ownership comparable to their current rented use, as far as I know. Which implies that alternative is not real.