I don't have the time to figure out the physics, but a body falling from, say, the 110th floor through the dead drop would be hamburger as soon as the chute began to curve. (Sorry, no disrespect to those who jumped or fell to their deaths.)
The only way it would work would be if the chute was at an angle all the way, which of course is hardly practical.
You apparently missed the part about the "drop bags", which would "catch" on the confined air in the tube as you fell, acting like a parachute, limiting the speed of descent even in the vertical sections, and simultaneously protecting your skin from scraping on the walls of the tube.