Maybe, but it’s a legitimately hard problem. Sort by lowest price legitimately means show the lowest price item first, even if it’s less relevant.
Based on other search systems I have worked with, they probably have an initial fast filter that limits the items from the entire inventory to a loosely matching set (erring on the side of including irrelevant items). Then a more intelligent and expensive ranking system would be used to find the best items from that set (where “best” means a bunch of things including relevance and profitability). Selecting “price: low to high” probably bypasses the intelligent system, so you end up with crap at the top of the list.
The low-priced items could be doing some kind of SEO scam to get on the list, or it could be something innocent like a fuzzy match to text in the description (could be a dumb issue like tf-idf that randomly exceeds a threshold due to noise).
You could argue that if they don’t prioritize the investment to fix these issues, it’s in some sense intentional. Nobody sorts by low price, because it gives poor results, because they don’t bother fixing it, because it’s not a priority, because nobody sorts by low price…
The problem is compounded by their seeming desire to always claim they have something
I did a search recently for a specific part. "39SF010". (a ~USD1.50-3 flash-ROM chip that is backordered til next year from "legitimate" vendors and from the manufacturer themselves). This is one keyword, and a pretty damn distinctive one. There's little room for there to be a "helpful" algorithm to fix my typing into something better.
With the default results, the first page contained 48 items. Exactly ONE was a relevant product. As a customer, I'd have been perfectly happy to see "results 1-1 of 1" and called it a day. But Amazon clearly didn't want to admit their warehouses are not infinite. There would be some potentially competent fuzzy match options there, but they whiffed it hilariously. Show me some other flash-ROMs, or at least other ICs, programmers, or breadboards, or those starter-kit boxes of no-brand resistors and capacitors... but they instead listed a bunch of toothbrush heads, a box of cookies, three random power bricks, a barbecue grille, flourescent bulbs, and a set of power tools running north of $1500.
> erring on the side of including irrelevant items
This is the reason for this problem. When searching for 'cat' and sorting by lowest price, the first promoted item doesn't contain the word cat and neither does the first actual result (but they are cat items).
If they didn't hoist 'legitimately hard' problems onto themselves, maybe they wouldn't need to solve them.
I would guess that adding fuzzy match to the candidate selection layer would result in better results after ranking with the default “Featured” ranker. Search teams tend to be pretty data-driven and likely have the ability to test whether a change like this improves revenue or some result satisfaction metric.
You can’t buy cats on Amazon, this is a poor example. But if you need the kittie fresh liter-o-magic model 2, then you will get the specific listings or nothing at all (garbage results as op said)