I'm really hesitant to name keeping one's mind unwaveringly on a task a virtue. I'm reminded of how mathematicians classically need to distract themselves after being stuck on a problem for a long while. There seems to be something very good that comes out of (1) priming the subconscious mind with a lot of potential updates and then (2) getting the conscious mind out of the way so that the subconscious mind can do some kind of magical processing in the background. (The same thing seems to happen with physical skills, by the way: I keep finding that taking weeks-long breaks from aikido sometimes boosts my skill quite a lot more than training over similar time periods does.)

Good point. I guess when I said “you are activating only the thoughts that are pertinent to the task at hand” I was referring to mainly system 2 thoughts because system 1 is not constrained by the same resource limitations. I would say that, in fact, habituating system 2 thoughts and making them system 1 or relaxing and letting your system 1 take over falls into the same idea of only activating the thoughts that you need to. If you continually use system 2 when system 1 can be used, then this can be a problem. I am sure that with aikido you don’t think through all the moves like a beginner would, but instead, like when we drive, a lot of the thought that controls your movement is done through system 1.