I'd imagine it'd play out pretty much like any other courier service? So long the couriers are plausibly not involved they're not gonna get in trouble right?

It's a boon for LE. They'll have access to the data. If they make enough fuss, they might even get Uber to encourage drivers to report suspicious activity. (What do they have to lose? No one wants to stick up for evil drug dealers.)

Remember how some of the Silk Road vendors were caught. LE found a couple suspicious packages confirmed to contain unlicensed medicines (supposedly via random inspection, but could have been secret spying, or regular gumshoe work). Investigators go to originating USPS office, look for suspicious activity. Quickly find it, make a bust.

Really, it should just point out the silliness of such contraband laws in the first place.