What if it is Black to move and he runs the h pawn down?
Very helpful analysis, vengence69. But on the 2nd/bottom diagram 11. c4 (instead of 11. d4) wins for White. 11. c4 Ke6 (11...Kc5 12. Kxe5) 12. c5 Kf6 (12...Ke7 or 12...Kd7 then 13. Kxe5) 13. Kd5 Kf5 (13...Ke7 14. Kxe5) 14. c6 & Black will lose his e-pawn giving White a decisive 2-pawn advantage. I think 5...Kd7 instead of 5...h1=Q+ is better for Black with drawing chances. It needs further analysis.
My basic reasoning I gave for the line in those diagrams was basd on two principles
1. The Black pawn and King would have an easier time of neutralizing the duo white is holding
2. moving the duo forward before securing the passed pawn from promoting was a slightly safer, though not as expedient line (Benko would say do in 20 moves what you can do in 2, apparently he had a good run with this idea, scoring endgame wins against both Smyslov and Petrosian in their heydays).
Still, you make a valid point. The win is a win whether you go by way of the Autobahn or a dirt road. Great insight.
In 1 I love endgames!
I've seen it before
end games need more concenteration