@Tolleys If there’s no public transport, then your situation absolutely requires it. There’s nothing wrong with people stating that sitters need a car in their listing. It would just be helpful to non-car owners to filter them out when searching on the site.
Many sitters do have a car, possibly most (correct me if I’m wrong), so I doubt you will have difficulty finding suitable people. No need to feel obliged to lend your car out. But this thread discusses car insurance for sitters: