Sean, I worked for IBM Research which operated explicitly on a stack ranking system.

BUT the stack ranking was done at the VP level, which represented almost 1,000 employees in a pool. Within your own team there was a tiny bit of contention only because your manager would have more and more trouble arguing that ALL of his people were all A players relative to other teams. But it was tiny, since some teams did indeed have many members getting a highest grade. Indeed if a team as a whole really delivered within a year, it was much easier for that manager to successfully argue the whole team was strong.

I do not know the details of the stack ranking at Amazon (do you?). In any case, stack ranking need not have the person-on-person competitive effect you describe.