That seems like a reasonable policy for Amazon to have. It's pretty normal practice for wholesale/distribution contracts to include clauses prohibiting the manufacturer from undercutting them in other channels after the contract is signed.

Why would Amazon want to bear the cost of people using their store as a free product billboard, or using their warehouses as cheap transient storage space, while trying to push customers to actually make their purchases elsewhere?

I'm not sure how this can be considered 'regulation' of the market, however -- to the contrary, it signifies that Amazon itself is sensitive to price pressure coming from competing distribution channels.

Amazon often have no idea what vendors sell their products for elsewhere. It's often an empty threat that vendors are very happy to ignore. Also, many of those agreements are spurious in international law. Unless there's a bullet proof contract with actual teeth, vendors will sell anywhere they can.