That's a cool idea. I wonder how many re-uses a box like that would take to make it cost effective over the same amount of cardboard. Should be feasible I'd think.
They did that with Amazon Fresh, and (at least from my perspective of several years ago) I think the asymmetry between # of packages and frequency of delivery didn't work out for them that well. We'd end up holding onto a stack of 4-5 crates for a week or so, which means Amazon would have to float probably a ton of these across their customers. That's all a guess though, but these days we get deliveries in plastic/paper bags, no reusable containers, so something must not have worked out.
That said, grocery delivery is much more "bursty" than package delivery.
Not necessarily. If the box costs 10 times as much, but they come up with a way to use the box 12 times, it was worth it.
That won't work if the recipient doesn't have a need to mail something back, but for a use case where you expected most boxes would be shipped back (maybe a phone repair company?), it could absolutely make sense.
The post you're saying "not necessarily" to has nothing to do with the cost of the box itself. If returning it costs too much, the box could be free and you'd lose money.