[Google employee, but AltaVista fanboy previously, been on the internet since the 80s and used all of these as they hit the market, and I remember the joy/excitement as each one hit in those days, like a moon landing. Also a DEC Alpha fanboy :)]
No way Altavista or Inktomi offered better result than Google. I was a heavy user of both, having adopted AltaVista mainly for similar reasons that I adopted Google, because AltaVista had way fresher and more extensive content than competitors at the time, it offered query modifiers, multi-lingual queries, and media search (images, etc), it even had Babelfish translation. It was obviously, unequivocally better than everything else before it. So the value proposition was unambiguous.
Google was similarly an obvious value proposition when it launched. PageRank was objectively better at returning the most salient results. AltaVista did ranking purely based on how the query phrase matched the index. As the Web grew, the amount of junk it would return piled up, it's easy to spam or game such a ranking algorithm.
As for Inktomi, you can read Inktomi's own employee account: https://www.searchenginewatch.com/2012/05/10/why-google-beat... Inktomi employees were using Google Search as their primary search engine. If you're not using your own product, you've got problems, how can you expect your customers/users to use it if you won't?
Yes, Google's brand is strong, and marginal returns in search quality mean most consumers won't notice the difference between engines, and will judge based on brand or UI presentation now. But to claim Inktomi and AltaVista matched Google Search results I think is rewriting history, when Google launched, the difference in quality was quite obvious and striking.
These days search engines have other requirements given how big the web is, how rapidly it changes, and how many adversarial attacks are made against it (blackhat SEO/webspam). You've got to have the infrastructure to index the entire web frequently, you've got to have a robust defense against spam, and you've got to have an even better ranking strategy beyond PageRank because a lot of the long tail may be good content, but doesn't have many authoritative sites linking to it.
There's still the possibility of someone upstaging Google, by building a search engine that not only indexes the Web, but has the reading comprehension to understand it, and understand queries from the context of gained knowledge. The first company to do that will kill Google Search, as the results will be self-evidently better. There are queries today that GPT-3 can do that Google can't, they're amazing when they work, mindblowing. If you can scale that to the Star Trek level computer, you win.
But you can't displace Google with a 2% improvement in results.