Searx is not a search engine with its own index, but rather, it is a meta-search engine, and operates by forwarding your query to a customizable list of other search engines (like Google, DDG, Wikipedia, etc) and gives you aggregated results. It is more privacy respecting, because the search providers cant run any tracking JS, see your IP, give you tracking links, etc. People may have their own instance for any number of reasons, including: hosting in different places to get different geo-specific results, to be faster by being closer to the end user, to change default themes/settings, to reduce the load on other instances. Nowadays, the fork SearXNG is more popular than the original.
doesn't that mean we have to trust the owners of the searx hosts though, if we don't spin up our own? I think i'd rather trust a faceless corp sometimes than someone with a potential axe to grind.
Big data is valuable, but little data is usually worthless. My instance is running on a Raspberry PI on my desk running Yunohost. If I figured out how to log IP addresses and the queries, I nor anyone else would have any use for the information. Searx doesn't set any cookies or do any browser fingerprinting. So all I would know is someone from an IP address (somebody in your house or on your VPN) queried something.
https://searx.space indexes most of the public instances.