First, just to clarify, because listings are stored in a "block pool," a new data structure that this system introduces, they disappear after they're no longer useful (specifically when the merchant who posted them is no longer a top merchant in terms of score or when merchants delete listings). This is in contrast to a blockchain, which generally is required to store all data forever even when it's no longer useful. This is covered in section 6.5 in the paper.

But of course, even with the ability to "forget" listings, you won't hit Amazon scale if every node is storing every listing. There are multiple ways to think about this.

The first is the argument that the Ultranet is still useful and highly-differentiated as the only private censorship-resistant marketplace, even at its initial scale (not unlike how Bitcoin provides a lot of value without scaling to Visa or Mastercard levels). Section 5.6.1 from the paper discusses this.

The second is the classic "we can always scale later" argument. For this, section 3.4 discusses how the Ultranet has much more incentive to scale than cryptocurrencies like Bitcoin and Ethereum due to the fact that it implements hyper-deflation, and section 7.3 discusses a more in-depth plan to scale the system by ~50x or more using the same mechanism that powers the built-in decentralized exchange.