It's probably possible to build a search engine for a specific vertical that's better than Google. However, you face a few really big problems that make this not worthwhile:
1) Speaking from experience, it's very difficult to define what "better" means when you don't have exemplars of what queries are likely and what the results should be. The reason search engines are a product is that they let us find things we didn't know existed before; if we don't know they exist, how can we tweak the search engine to return them?
2) People go to a search engine because it has the answers for their question, no matter what their question is. If you had a specific search engine for games, and another for celebrities, and another for flights, and another for hotels, and another for books, and another for power tools, and another for current events, and another for technical documentation, and another for punditry, and another for history, and another to settle arguments on the Internet, then pretty soon you'd need a search engine to find the appropriate search engine. We call this "Google", and as a consumer, it's really convenient if they just give us the answer directly rather than directing us to another search engine where we need to refine our query again.
3) Google makes basically 80% of their revenue from searches for commercial products or services (insurance, lawyers, therapists, SaaS, flowers, etc.) The remainder is split between AdSense, Cloud, Android, Google Play, GFiber, YouTube, DoubleClick, etc. (may be a bit higher now). Many queries don't even run ads at all - when was the last time you saw an ad on a technical programming query, or a navigational query like [facebook login]? All of these are cross-subsidized by the commercial queries, because there's a benefit to Google from it being the one place you go to look for answers. If you build a niche site just to give good answers to programming queries or celebrity searches or current events, there's no business model there.
Funny, I don't disagree with this, but my perception has been that Google seems to detect when I've switched roles from one type of programmer to another. I don't know if that's organic from the topics I'm looking up or not, but if I'm looking up a generic string search, it seems to return whatever language I've been searching for recently. (very recently in fact)
My point is, it seems like the search engine intuitively understands my "vertical" already. Maybe it's just because developer searches are probably pretty optimized.
Google Ads (used to?) lets you target by "bahaviour" vs "in-market". They can tell the difference between someone who is passionate about beds, maybe involved in the bed business (behavior) and the people who are making the once-in-a-decade purchase of a bed (in-market).
Google can tell devices apart on the same google account and keep together search threads. I might be programming on my desktop making engineering searches but at the same time I'm googling memes on my phone; both logged into the same account.
Better is a search engine that takes your queries more literal. This is what everybody means when they say Google used to be better. The query keywords and no second guessing.
When you insist on Google using verbatim mode or something, you often don't get results. Which is bullshit because I remember 10 years ago, queries like these had me plowing through the results, so much that you actually had to refine the query -- you can't do that in Google any more, at least it's not refining, it's more like re-wording and re-rolling the dice. But it all feels very random and you don't get a feel for what's out there.
I mean sure there is a place for a search engine like this, if it works well. And in its own way, Google works well.
I sometimes do want my query to be loosely interpreted like I'm an idiot, and I head straight for the Google. Ever since I saw the "that guy wot gone painted them melty clocks"-meme, for certain types of queries I have indeed found that if I formulate my question like I got brain damage, I get superior results. Because that is the kind of audience Google wants you to be.
But sometimes you don't feel like the lowest common denominator and you don't want to be treated as such. And there should be a place for that, too.
I can't get better products by searching Google, I can get the best-spammed products or most promoted products only.
The fact that I am getting low-quality service and Google is printing money means that there is a place for good a good service and if that service cannot emerge due to Google's practices, it probably means that the regulators need to take action.
Or maybe the search is dead, long live social media.
The gist is, I am not happy with a service but the company that makes that product makes a lot of maney. Can't tell if I am an anomaly or if other people feel the same way because Google is a monopoly and maybe the regulators should make it possible to compete with Google and see if there's a space for a better service.
Yes yes, I am the product but I am the product only if I am happy with the stuff I'm getting in return.
Keep in mind when Google started, Yahoooooo! Was the big player and Google overtook them by simply being better
Definitely have seen malicious adds for "facebook login", though that was probably 2016 or 2017.