I've been trying to think of better, less centralized solutions, and they're not too hard to imagine. An open transportation marketplace, populated by independent vendors, isn't so far-fetched. In fact it'd probably look quite similar to Craigslist, except with better handling of user identities and reputations, and a much better mobile-focused user experienced. Anyone could list a delivery service in one of a number of different categories, with custom price rules, and categories might include taxi/human transport services, food delivery, package delivery, etc. A review system, payment integration and mapping would come built into both the provider and user's mobile apps, but insurance etc. would be up to the individual vendors. Fees for listing services would be nominal, and almost all the revenue would go directly to the vendors themselves.
The trouble with this kind of service is that it'd end up being quite a bit less safe and quite a bit more messy than interacting with a single company like Uber. But the lower transaction costs should make services significantly cheaper, and power would be much less centralized.