Having worked at Google’s Search Quality Evaluation team, I can confirm that Google would only manually remove sites from its search results if they violate its webmaster guidelines: https://support.google.com/webmasters/answer/35769?hl=en
Of course, there can be other issues preventing a site from showing up in the search results (e.g. site migration issues, accidentally locking out Googlebot in robots.txt, ...). In such cases, the best way to raise the issue would be to report it on the webmaster forum, which is frequented both by smart and helpful users and by Googlers working on search quality: https://productforums.google.com/forum/#!forum/webmasters
Having worked at Google’s Search Quality Evaluation team, I can confirm that Google would only manually remove sites from its search results if they violate its webmaster guidelines: https://support.google.com/webmasters/answer/35769?hl=en
Of course, there can be other issues preventing a site from showing up in the search results (e.g. site migration issues, accidentally locking out Googlebot in robots.txt, ...). In such cases, the best way to raise the issue would be to report it on the webmaster forum, which is frequented both by smart and helpful users and by Googlers working on search quality: https://productforums.google.com/forum/#!forum/webmasters