Price's law is of questionable empirical validity, it's more like a useful guideline/urban legend. On the other hand, there is substantial economic research demonstrating the harms of monopolies, including vertical ones.
I'm a bit confused. Are you claiming that because of Price's law, Amazon doesn't actually benefit from it's monopoly position?
Almost. I think that Amazon cannot hold a monopoly position in all markets because its size would be so big that a smaller competitor could compete.
As a consequence, there will be an optimal size where Amazon is serving many markets, most likely the most profitable ones, thus massively benefiting [ * ], but they leave every other market open.
Depending on the future, this is not necessarily a bad position because low interest rates could seed plenty of startups which means that competitors could operate below break even points.
The question is: will Amazon ever reach that position or will its competitors make sure that all its profitable markets will dry up and its growth will be limited?
[*] Actually, not Amazon is profiting because the value of that dominant position would be priced into Amazon shares in advance. Amazon would just execute its dominant position that its investors had foreseen.
I'm a bit confused. Are you claiming that because of Price's law, Amazon doesn't actually benefit from it's monopoly position?