How is Amazon forcing them to raise prices on other platforms pro consumer? The only one who benefits from this arrangement is Amazon, everyone else including the consumer just loses out.
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.
In a free market sellers will leave the Amazon ecosystem and move to a platform with less restrictive agreements, resulting in lower consumer prices (albeit with less availability). That’s exactly what GP is arguing. Obviously GP believes in a free market.
Amazon’s belief in their own market power is irrelevant.
It does, since losing sales on Amazon costs them more than raising the price on other platforms then that is what they will do, since companies are motivated by profit. Amazon knows this, that as a dominant market player if they add this rules the vendors will have to abide it since they will lose more from not using Amazon.
This is how anti-competitive practices works and why we have laws against them.
If they decide to raise prices, then that has more to do with the seller than Amazon.