Clearly you are not a believer in free markets, because by the theory of free markets these prices would naturally arrive at the lowest possible price all on their own.

You are right that this policy is very simple, it's very clear both mathematically and logically. Companies cannot lower their prices lower than their costs. If costs are variable across platforms but prices are fixed to a single value than this will de-facto result in INCREASED prices. If this policy causes someone to leave a platform, that STILL doesn't result in prices any lower than they would absent the rule.

In fact, the sheer existence of the rule is a clear statement from Amazon that they believe they have significant and durable market pricing power, since if they didn't, this policy would clearly lead to sellers and buyers leaving their platform.