I agree that the time pressure is both a pain, and central to the challenge. If not for the effort to solve in fifteen seconds, I would not have missed any of those I've tried. It should be restored.
Tactics Trainer time used

Ziryab, you can try playing the Tactics Trainer in the unrated mode. In the unrated mode you will not have the pressure of the time limits and restrictions and you will be able to focus more on playing the best moves and finding the truth in each position. You can change to this setting at http://www.chess.com/tactics/settings.html
I noticed that the clamoring about time pressure in tactics trainer has led to the removal of the timer bar beneath the problem as you solve it. (I actually think this is a useful training tool.)
Instead, can we get a "time used" statistic after we've solved a problem? Right now we get a list of "My Rating", "Probleml Rating", "Avg. Time" etc. It would be nice if that list included an entry for how much time I used when solving the problem.
I know I can use the score to get a sense of my time relative to the average time, but that is less straightforward.