I don't want the search engine to do math, find flights, or look up bus schedules; I want it to find me a calculator site, find a site where I can look up flights, or find the page with the bus schedules on it. I don't care what the search engine's opinion about those things might be; I care where the authoritative sources live.
Fuzzy spelling-correction search can be useful.
It's true however that most people do not want the search engine to know much about them. Interestingly, most user do notice (and complain) if a search engine stops using personalization and localization. When given the choice between more privacy or better results, the vast majority opt for better results.
I have no idea what personalized results look like, to be honest. I switched to Google in part because they didn't pester me to log in like many of the other search engines at the time; now that Google has succumbed to login disease I've moved on to duckduckgo.