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Of course you can debate almost anything, but there's this word "general" in GPP.That's controversial.
My heart rate spikes higher doing a set of 5 or 10 2HS vs 1HS with the same weight.
1HS certainly gives you the anti-rotation benefits but I think you can express more power in the 2HS. As to what carries over best to GPP? I have no idea at all.
GPP-training should prepare you for a wide variety of things and build a big base for your SPP (if you have such aspirations).
1H-Swings simply build more things. It's not like they don't improve your power output. They do, just a little bit less than 2H-Swings, but they also yield the anti-rotation benefits, which 2H-Swings don't train at all.
So we have a version that builds 2 qualities versus a version that only builds one. Even though it builds the one quality slightly better than the other version it's still no question which version is better for GPP.
And I'm not even including the higher recruitment of muscles and the better grip training in 1H-Swings.
Slightly higher HR? It's debatable whether that's even a good thing.
I'm not saying you should stop doing 2H-Swings. In the paragraph from S&S that I quoted, Pavel even says you should do both. What builds more power than 2H-Swings? Shadow-Swings with your 30% bodyweight KB! Guess what's included in S&S.
For GPP the majority of your training should be done with the version that builds more qualities and that simply is the 1H-Swing and IMO that's why Pavel chose it as the version you use the most in S&S.