One aspect that Uber seems to have over-looked is that bike messengers traditionally rely on a network of relations, and commitment to the job -- it’s not a very gratifying job, therefore very low chances of finding another employment, legal or not, are qualifications. This allows the dispatcher to hire anyone with a pulse and calves, but trust some more and have them handle the occasional key delivery.
An truly Uber-like equivalent for parcels might be problematic. Imagine a couple of company shills, posing as a putative messengers, near your competitors’ headquarters.
If they compete on price and keep the same quality of delivery service - my guess is they'll be fine. Or current bike messengers will just join Uber as it's an extremely powerful lead generation tool, similar to cleaners and Homejoy (as we've seen at least some small level of cabbies joining Uber - I don't have hard numbers, but I have at least one anecdote that this has happened before).
