In reality, Amazon are incentivized to sell you more stuff, so allowing them to calculate ratings through some mysterious black box would introduce perverse incentives (i.e. Amazon is incentivized to sell more higher-margin stuff - would they be more tempted to inflate a product that is actually a '4 star' to a '5 star' to close the deal? Also how can we be sure that their black-box algorithm doesn't generally inflate Fire tablets and deflate iPads? This can happen even if the algorithm is entirely open).
Secondly, would probably reduce trust in the product rating system (as it will be necessarily opaque and hard to understand compared to the existing approach of averaging the reviews).
Amazon won't even fix basic review gaming - not because they can't (otherwise they would have acquired Fakespot) - but presumably because fake reviews help with sales.
If Amazon had a ratings black box, they would not be incentivised to be fair with it.
But a simple-to-understand ratings system may help sales more than an untrustworthy-black-box calculated rating (particularly considering reviews are about trust).
The real fix is to not have a single global rating for a product, but instead have 'personal ratings'. Ie. Every product rating I see is either a rating I have given, or Amazon's best prediction of the rating I would give if I had bought that product.
Such predictions are inherently hard to game, since if you start artificially rating your friends products highly, then the system will show high ratings only for your friends products to you.
Then they can do things like "I see you bought this product thinking it would be 4 stars, but you actually gave it 2 stars. We apologize for getting it wrong this time - have a refund of half the purchase price". That gives the AI team plenty of financial motivation to get the ratings correct.