It can work, just not in a way that Silicon Valley VC bros want it to.
Most countries already have a legacy version of this system in place: the post office, as well as a few private courier companies. Those systems' "tick rates" are typically one day - packages are collected at depots/sorting offices early in the morning, assigned to couriers who then spend the rest of the day delivering them.
Increasing the tick rate of such a system is possible especially with smaller goods as well as being able to take advantage of more "depots" (for grocery deliveries, supermarkets are essentially the depots) - the costs will obviously be higher, but not prohibitively so.
The problem with the current delivery services is that it's fragmented - every company has their own couriers, restaurants/supermarkets, etc where not only is the supply & demand unbalanced, leading to situations where one company's couriers may be sitting idle wasting time loitering (leading to potential antisocial behavior) where anothers' might be overloaded and delivering a poor customer experience with regards to wait times. The system also has the overheads of people staying idle which is currently subsidized by treating these workers like shit and denying them employment rights/benefits.
A single marketplace providing an API for moving goods from point A to point B priced by weight, special requirements (refrigerated transport, etc), timeliness and the current state of the market (dynamic pricing) could work. This will allow the system to maximize the efficiency of the people on the ground, being able to consolidate deliveries and reduce waste (bikes or vehicles sitting idle, couriers loitering around, etc). This could be operated by the existing postal system and even use this same infrastructure for mail/package delivery.
The above system would undeniably cost more than the current VC-subsidized services which also underpay their workers and treat them like shit in general, but not by an exorbitant amount. Its costs overheads would scale linearly though which is a bad fit for VCs looking to monopolize the world, however as a public service similar to the post office it should be viable.