Why shouldn't they be allowed to do this? If you want to sell on their market, you promise not to undercut them.
Amazon exists as a discovery tool for consumers. They don't want third party sellers to get free advertising. That isn't anticompetitive.
It is no different than Nike, who requires no discounts on specific products, etc. Amazon isn't prohibiting selling on non-Amazon platforms. Amazon is prohibiting undercutting them if you choose to sell with them.
How is that anti-competitive?
Yes, they are. They are using their influence and market power to prevent others from competing on price, using the threat of economic retribution on their platform. If this isn't anti-competitive, then nothing short of sending assassins on your competitors is.
It is the exact same thing as is argued by social media companies: they have the right to moderate the content posted on their platforms because it's their platforms. You can do whatever you want on your own site.
Yes, companies cannot influence behavior of people or businesses that have no business relationship with them, direct or indirect. In other words, you are saying that indeed, the only anti-competitive action is sending armed thugs to sabotage your competition. Everything else, every contractual condition, is fair game.
I'm saying that entering a voluntary transaction knowing the terms of the trade does not amount to anti-competitive behavior. Nobody forced you into the trade. Nobody prohibited you from entering the trade.
Entering the trade with clear conditions is voluntary. You could easily just not do business with that partner. Here that would be not using Amazon's marketplace.
You do realize that, by this definition, nothing short of fraud or forcing someone into a contract at gunpoint, could qualify as anti-competitive?