Mathematically, you are likely correct. However, 'tweedle dee' and 'tweedle dum,' my lungs, beg to differ. Each time I have done this, they threaten to make an appearance via he oral route...
Don't forget to factor in the added effort of lifting the rucksack weight every time you take a step on a upward incline. It DOES add up. Imagine you have your rucksack on, and you are on a powered treadmill. Set the treadmill at about 1 10 percent incline and a 2.5 to 3 mile per hour pace and try to walk 5 miles / 8 km...
I think you will soon see my point...or YOUR lungs... the end, I submit it is about felt effort and strain, NOT just distance. This slope/felt effort paradigm applies to any vertical(ish) route.
I am not being argumentative. What I am saying is that after doing the
Camino Frances from SJPdP personally twice, my wife (after seeing the road down into SJPdP from Orisson from a car as a tourist this past August) made be SWEAR to her that I would NEVER do it again.
Me being 65 she is afraid that I will have a heart attack from the effort. I note in passing that I have no CV conditions or symptoms, risk factors, other than carrying too much weight.
However, being married 40 years this coming March, I have learned which fights to pick. This ain't one of them. So, the next time I do this, I will taxi from SJPdP to the stone cross at the 10 km point, where the route hands a right towards the frontier with Spain.