Uber already has specialty delivery services in some markets. Here in NYC they have UberRush, which is a bike messenger service, and they have UberEats, where they have a different restaurant each week available for delivery using Uber.

It's also long-standing practice in cities like NYC to use car services as couriers for places that bike messengers or on-foot couriers can't easily reach.
Law firms and investment banks use them all the time to deliver time-sensitive documents to VIPs in the suburbs. Restaurants and specialty food stores use them to deliver beyond their regular bike-based delivery zones. Using Uber for that purpose is no different than any other car service.