In the case of Uber and Lyft, that's all the technological infrastructure that goes into making the platforms work. This isn't a trivial amount of work that can be easily replicated by taxi companies or scrappy driver-owned coops, as attempts to do so have shown. As we're all familiar with, maintaining this infrastructure is also far from free or trivial.
Credit unions are an instructive example. Many offer membership in interoperative networks, but few are able to effectively compete with the customer-friendly offerings of big banks with centralized power structures. The ability to satisfy customers isn't some side-effect, it's a key goal. A localized organization that can't compete is worth nothing except as a cautionary tale.
With that in mind, I would say the organizational challenge of coops is thus: how to keep centralized infrastructure controlled by localized entities while being competitive with non-local entities.
So, this problem can be addressed by cooperatives, it's just a different kind of structure that distributes power locally -- with centralized power deriving from the bottom up, by the membership of localized cooperatives. The organizational challenge for expansion is how to avoid administrative capture: how to keep centralized infrastructure controlled by localized entities.
I don't think this "franchise" challenge has been worked out with platform cooperatives. However, if this NY based cooperative becomes profitable, it could expand to other cities not by getting bigger, but by forking off the operational aspects into a cooperative-of-cooperatives, then, a Chicago driver's cooperative could be a member of this shared operational entity.