why is the Tactics Trainer timed? In studying tactics is it important to measure how fast one can find the solution? I am unfamiliar with other sites is this common? Are endgame studies timed?

Yes. Try Chess Tactics Server if you want less time and a much smaller board. You can always ignore the rating and just solve the problems if you want no timer.

In real games, decisions must be made under pressure. The faster you recognize patterns, the more likely you'll see them in real games.

I find chess.com is more then fair on times. Go to tactics server and watch the time flash by.

I would not worry so much about the time, and more about if you got it right or not. Speed will come.

Agreed, initially it is more important to learn the tactics regardless of time but, if I understand you correctly, it seems that with the Tactics Trainer the ultimate goal is to recognize a pattern that triggers your (correct) response, i.e. less 'calculation' and more pattern recognition as you become better, yes? Hence the time measurement?