I don't think they care about HA at all, but they do care about Amazon not going through them to get access, and from the API server's perspective, both look identical.
Personally, I hope that Amazon doesn't play ball. You can TRY and seek rent from the world's largest retailer, but you need them, they don't need you.
My main takeaway is that Amazon should offer a discount to deliver packages to buildings with staff to accept the packages. They never go missing, so less refunds, and the building staff does not charge Amazon to receive packages.
The business dynamics are pretty interesting, though. It could be that paying this company reduces missing packages so much that it actually saves Amazon money, which they pass on to consumers in terms of lower prices. Or, it could be that they charge $1 per access, and Amazon passes that on to the customer, and then people are disincentivized from using Amazon. Meanwhile, a competitor (say, Walmart?) brokers a deal where they hide that fee, and take enough customers away from Amazon that Amazon has to play ball (and now the price is $2 per access). Costs go up for everyone.
The phenomenon of partnerships like my hypothetical above are very interesting to me. Every so often I check what I can use my credit card rewards points for, and most of the offers, to me, seem like "failing retailer desperately needs a customer" rather than anything I actually want. Thus, the partnerships must be a pretty important tool for companies that are not in first place.
Finally, I think about the long term effects of this sort of thing. Everyone wants a % of every transaction. "Oh, you turned your lights on when someone came to deliver a package? Pay the manufacturer of the light bulb $1 and your electric company an extra $1." This will look like "economic growth" to each of those intermediaries, but in the end, they just devalued the dollar. ("Inflation.") We end up with bigger numbers, but actually decrease the amount of "value" floating around.