"Sure, you end up beating them about half the time if you cut the search down enough but it generally feels like they were still outplaying you for much of the game and you won because they made one or two blunders."
That is what winning in chess is. Minimising blunders.
I believe that observation is borne out in the statistics too, but traditional chess training usually centers around finding the best, hard-to-find move in a position rather than avoiding blunders. I think it would be great if there was more blunder-avoidance training. In other words, a normal position where a blunder looks attractive but the player needs to avoid it.
That is what winning in chess is. Minimising blunders.