Huh? It's a ranked retrieval model. Each result has scored a little bit worse on their relevancy function than the one above it.

To not trust that the results on page 1 are better than those on page 34557 is the same as saying that their ranking function does not work at all, which would mean that it's at best as good as random chance. That's clearly not the case, therefore I can trust that page 1 indeed has more relevant results than page 34557.

With that said, Page 34557 doesn't exist. And that's fine. The result count estimate is not based on the actual ranking that has taken place (at least not directly). It would be an absolute waste of resources to rank that many results. If you cannot find what you're looking for on the first page, then it's much easier to reformulate your query. Easier for you because it gives you more control over what you want your search results to be and easier for google because it only needs to rank a couple hundred results instead of a bajillion.

Well, one could claim that indeed their ranking function does not work well - at least recently. Stuff that is relevant rarely is showing up on the first page as it is losing to various spam sites having articles written by AI so that it can match the typed search query and get a good ranking, but articles themselves being misleading and incorrect. I remember the days when you could really dig deep into results pages. Maybe not 34557, but above 100 you could get niche human written content on the interesting topic.

Yeah, I used to pretty frequently click through, and find relevant/useful content, some 20+ pages in on paginated web search results. Well, unfortunately the major search engines have changed their functionality such that there's usually no point in even looking beyond a couple pages (or, arguably, even looking at the first page for that matter).