From my experience implementing search using Solr (or Elasticsearch) is simple to get the basics and hard to get really really good.
So I guess most developers/companies are satisfied with "good enough".
I had this problem recently and I figured that I was trying to find a solution for a problem I didn't even have.
I decided to just not use any form of captcha. If it ever becomes problematic (e.g. spam) I can still implement a captcha again. Until now it works perfectly fine.