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.