I feel your pain Bartleby. The idea behind the tactics trainer is to test your pattern recognition skills; so no, it's not quite the same as intuition. The problem of course is that while good players have absorbed these patterns, the rest of us are screwed. And yes, I agree, that "guess and click" seems to be the only thing it's teaching lower rated players.
V3 will supposedly partially address this issue by no longer penalizing correct answers. You may not gain any points, but you will never again lose points for a correct answer. We'll see if that actually makes the final cut. I have my doubts, given that really good players love the TT just the way it is.
You can of course play it unrated (unless that's a premium feature ?), and I do that periodically. It doesn't feel the same though and I usually tire of it. Coach Heisman is a strong believer that mastery of basic tactical patterns is key to advancing your skill and has his students use Bain's Chess Tactics for Students. It's a relatively easy book of tactics but Coach wants you to be able to immediately recognize those simple patterns. It seems like a logical approach and I've had some success with it.
So what I do is periodically reset the TT. I usually deliberately lose the first question which kicks the problems down to below the 1000 level and then claw my way back up to my level of incompetence, which seems to be around the 1500 mark. Many of course have simply given up on the TT and train elsewhere. A simple Google search for "chess tactics training" or somesuch will show other sites. Good luck and rest assured your dislike and distrust of the TT is shared by many.
I have used the chess.com tactics trainer for quite a bit, but have stopped doing so because the rigid clock is ticking me off. I am more successful with tactics trainers from other sources where there is less time pressure.
I get the feeling that the chess.com tactics trainer rewards people for making intuitive, rather than calculated moves. People do not get rewarded if they take their (reasonable) time calculating and then coming up with the right conclusion. Instead, they are encouraged to make an intuitive move. If they get it right, points for them. If they calculate it out, get it right, much fewer points. I feel it teaches bad habits.
I do know that stronger players need less time for calculation. I understand that strong players also need training.
I just feel that people who are not that strong yet should not be lured into making hit-and-miss intuitive moves.
Not everybody is a blitz player and needs to make very fast calculation. I think the clock has its place in chess, but the tt clock is a bit exaggerated.