I definitely agree. I have a slower brain than some, and by the time I have figured out the position it's often simply too late to make my move. So I end up panicking and making a hasty and incorrect move more frequently than I want to admit. If I knew that the system was tracking my correct answers even if I ran out of time, I would be able to relax and take my time.
tactics training suggestion

P.S. However, I should add that I believe the idea of the tactics trainer is to train you to think more quickly. It might be counterproductive to allow us to slow down?

This is an eternal debate : solve 'em quick vs. take your time and get it right.
I'd side with the "solve 'em quick".
Why? Because unlike real "in game" chess positions, you know there's treasure buried here, there's a target with a bullseye in this position SOMEWHERE. You really are only exercising your pattern recognition skills ... nobody's going to give you a cookie for solving the problem in 5 minutes because you can theoretically brute-force your way through anything if you know there's a shot in here.
The training is to help you see basic motifs quickly so that you can re-use them in actual games...if you are playing fast and accurately with "instant recall" and pattern recognition, that's a "desired" behavior (that strong players display) and the system rewards you for it with more challenges. if you are slowly calculating forcing lines because you haven't seen them before, that is "less than desired" behavior and the system will "reward you less" and keep you away from tougher problems until you start using "recall" more often than brute calculation.
The points/ratings you accumulate are the only way chess.com figures out how to adaptively challenge you with easier/harder problems.
If you didn't provide feedback to chess.com via a competency score, how would it know NOT to hit rank beginners with complex mulitple-motif problems or NOT to give titled/expert players basic knight forks?

I'm not saying to change the way the tactics trainer works. I'm merely advocating an additional measurement that I believe many chess.com members would find useful and make the site more to their liking.
That said, I agree more with the "take your time" folks on this topic. I've seen some posts that say if you don't see the move in 10 - 30 seconds, you probably won't. I think that's baloney. If that were true, what would ever be the use of playing with a time control beyond 10 or 15 minutes? Some people prefer to be able to think through all the variations before selecting a move that just looks right. For those people, being able to track the percentage of problems you've solved correctly, regardles of the time required, would be useful. There would be no drawbacks of having the additional measure, and I'm betting it wouldn't take the programmers at chess.com very much effort to install it.

I am not very good at the tactics trainer. I often run into time pressure too on the tactics and in games. I do not think as fast or as instinctually as I wish I could.
That being said, when the tactics trainer challenges me with tougher tactics that I don't complete on time, the easier ones start seeming easier--and I am solving them faster. I think the program does its job well in teaching you to have more rapid pattern recognition.

if you go to your "My Tactics Trainer" screen there is a breakdown of your stats that gives you the % you have gotten right and the % wrong.
Tactics trainer plots your "rating" for different time scales. How about adding a plot for % of tactics problems you solved correctly? This would be very helpful for those who don't like the timed problems and would give another measure for tracking progress.
Anyone agree?