The "buy box" is a product-level feature, not a seller-level feature. On any given product page, there may be multiple sellers with offers (one for $9, two for $9.50). The $9 offer would be prominently displayed in the buy box and the other two would be in the "other offers" section.
If another site starts selling the same product for $8.50 (regardless of who the seller is), Amazon may hide the buy box and put all the offers in the "other offers" section to avoid advertising an offer that isn't the best price available online.
Consumers price compare across sites, and Amazon wants to maintain its reputation for low prices (and in truly egregious cases prevent sellers on Amazon from price gouging).
Except they do the same for non-new products which muddles things tremendously.
If I don't see a price I assume it is out or they only have used ones. Certainly occasionally I have seen scalpers when I double checked anyway to see what the price would be if it returned but generally Amazon caught maybe half the scalpers in my experience.
Having a signal that means "you could get it less elsewhere" be the same signal as "I only have scalpers" isn't exactly good for consumers.
Also this implies that Prime shipping is worthless given they exclude it from the calculation...
The max price filter in the left margin is worth the effort to find the same product selling cheaper but only displayed a few pages later than than the primary search results.
Is buying from the buy box ever to the customers advantage?
If another site starts selling the same product for $8.50 (regardless of who the seller is), Amazon may hide the buy box and put all the offers in the "other offers" section to avoid advertising an offer that isn't the best price available online.
Consumers price compare across sites, and Amazon wants to maintain its reputation for low prices (and in truly egregious cases prevent sellers on Amazon from price gouging).