The point people are trying to make is that walkers can deliberately look for reservations during the absolute slowest travel periods, where competition to get rooms is significantly reduced. Yes, on that specific first day of their walk they are 100% first come first served, but choosing to start the walk at the slowest travel periods of the year, then moving forward to busier travel periods does present an advantage over someone not walking who tries to get those busy periods exactly at 11 months.
As has been said, if there was absolutely no advantage to walking, then no one would be doing it.