Additionally, by running a private instance you have effectively given all these companies a spotlight onto YOU. Only your searches are going to come from that instance and these companies already have enough information they can figure out WHO is making that search pretty much right after you click through the first result.
Just from the available public instances you can quickly see that other search engines may block your requests for one reason or another but your server will be constantly retrying to query them from time to time. Last thing I want is to find my IP addresses on some sort of "naughty list" because I wasn't honoring some 403 error my server was getting every time I searched something.
There is nothing that says other search engines won't wise up and figure out how to stop searx from "abusing" their search functions so it almost feels like the only sure way to ensure search privacy is to run your own crawler, for better or worse.