I disagree. During a chess.com deathmatch on chess.com tv, IM Danny Rensch and IM David Pruess both saw a blunder on the board at the exact same time, in about 2 seconds. One of the reasons for tactics training, the way I understand it, is to instantly recognize a mistake by your opponent, and then cash in.
Disagree all you like, but unless you have video evidence of the Hallelujah Choir, you are wrong. The two IMs saw the shot, but that doesn't guarantee you will after using the tactical trainer. I am not arguing that titled players are very good at tactics. I am not arguing that tactics skill is not important. I am arguing that training yourself on known winning positions is not sufficient. You can traing all day long, but without practical experience, you will miss a lot of opportunities in real play.
A large percentage of chess positions don't have any tactical shots, if you don't know the basic principles of strategy you will be wiped out by any GM.
I don't know what percent of chess games have no tactical shots, and I'm not sure if anyone really knows. At the highest of levels (Super GM), I am told that even though I can't see any 1,2,3 -10 move tactics in those games, they are imbedded deep into the games, with tons of prophylaxis built into each position, to avoid the tactical shots.
If I were to step in and make one move for one of the Super GM's, say at move 30, the position would most likely go from equal to dead lost, with a tactical shot hitting me over the head, because I can't see all of the crazy hard tactics at work behind the scenes in the position.