It's a reasonable response: that driver isn't delivering groceries to you, they're delivering to your whole neighborhood. As the density of delivery orders goes up, there's more and more opportunity to batch nearby orders like this.
In addition: if you pre-order a bunch of deliveries, you're giving the delivery service more cash upfront. That usually allows for greater efficiencies in how the cash is spent and/or invested in the business.
Of course, if they never reach the break-even density, the whole thing is doomed to slow failure.
While the post you're responding to doesn't explicitly state all the detail you were looking for, I do think you're being a bit too dismissive.
Not sure on the accuracy of the claims, but the "hand waving" is saying that the estimated time spent per delivery may be a large overestimate if that driver is delivering multiple orders per trip, thus reducing the amount of time that a single customer pays the driver to drive out to a specific area. Point number two was to imply that, yes, if they priced a delivery at $2 per delivery, they probably are operating at a loss, but not everybody gets 50+ deliveries in a year, thus bringing the average cost of delivery up. Heavy users have existed in other systems and they didn't become suddenly untenable (Amazon prime seems to handle it just fine).
It needs a bit more detail. Is the assumption of groceries once a week really weak? (literally everybody I know gets groceries once a week)
Is the density of drivers and customers such that drivers deliver at a rate <<15 min?
"Not everybody gets 50+ deliveries a year" can sound as sensible as "Not everybody brushes their teeth every day" or as pedantic as "Not everybody sleeps every day" depending on the underlying statistics.
In addition: if you pre-order a bunch of deliveries, you're giving the delivery service more cash upfront. That usually allows for greater efficiencies in how the cash is spent and/or invested in the business.
Of course, if they never reach the break-even density, the whole thing is doomed to slow failure.