I will literally never want to play an engine user

That's a completely different issue from what I understood before. Yes, it would be useful. Anyway, known cheaters cannot play rated games. Why don't you use that mode play?

Unrated games are a little less stressful for me because I am a competitive person

In the "Create a game" pop-up there is a checkbox giving players the option to select to play unrated games against "members only". Maybe an additional check box could be added, called "humans only" or something similar? :-)

I guess there could be an option to not be paired with players without established rating in that category..

Hmmm...yes this is an interesting idea. Obviously you can't ever play a rated game with an engine user as they are banned from such play, but they are still allowed to play casual games. Obviously some people likely would want to filter those players out of their casual games as well. Maybe engine users should have the same classification flag in the filter as anonymous users so that they are removed with the same filter as playing members only? Or maybe their rating should be set to 0 rather than 1500 so that they can be filtered out by rating. I think either of these is a fairly simple and valid solution.

Fenris has a good point, treating confirmed engine users an anonymous would make sense. You know that when you search for a game and allow anons to accept the challenge that there is potential for cheating.