I don't get it. All the alternative carriers are obviously in their system already, since deliveries obviously get routed via all of them, and (presumably) some algorithm selects which one that is in each case. All it takes is to put one more selection field on the order (and I guess in the customer profile, for a personal default value) and then use that if provided and the algorithm only if not provided. What's so hugely complicated about that?
I've certainly been part of something very similar, where a company has multiple suppliers providing the same service. Near contract renewal time we would move our volume on their competitors to remind them that they needed us more than we needed them. It was a very effective way to get them to keep lowering their prices as the years went on.
There is also probably also a logistics piece as well. Amazon will be shipping products to carriers last mile hubs or similar themselves, rather than having a carrier handle the entire distance. Which makes it cheaper for Amazon. So carrier will also be picked based on which hub is nearest to one of Amazons warehouses, how full the Amazon truck going there is, which warehouse has the product etc
Maybe it’s in fact trivial, but at Amazon’s scale I find it hard to imagine that any changes to their shipping algorithms are that easy, at least compared to the increased revenue that goes along with it, which in this case presumably is zero.
If you’re willing to put up with all of Amazon’s other crap in exchange for convenience, you’re unlikely to drop them because they won’t allow you to pick the shipper, at least until someone else starts taking business away from them.
I assume because the volume of returns is much lower than the volume of sales, plus Amazon isn't responsible for coordinating the return.
In essence, my suspicion is that at Amazon's scale they literally can't afford to let customers pick their own shipper. That's one variable too many to manage for their massive logistics problem, and the expense of building out the support for that would never be recouped.