Well, it does kill the process but "corespotlightd" is automatically restarted again by the operating system. That's what's supposed to happen. "corespotlightd" won't disappear forever because of this auto-restart. [NOTE: when you first go looking, you may have more than one "corespotlightd" process running. Check the PID column and make sure you kill both of them and don't end up killing the same process twice - or how ever many you have running.]
...but that's the intended behaviour: killing the process and letting it auto-restart can - for some people - restore the search capabilities. YMMV, sorry.
As you see, this process is quick so, if it works for you but SEARCH begins failing again,, just repeat.
FYI:
"corespotlightd": https://forums.macrumors.com/threads/what-is-process-corespotlightd.2187256/
In any case, since Apple doesn't track this particular discussion thread, may I suggest that you also report this problem (and your frustration) at https://www.apple.com/feedback/mail.html [select Bug Report from the Feedback Type popup] This is where Apple expects to get Bug Reports...... if you haven't already done so
Thanks.
Wayne