To throw for maximum distance (on an infinite plane in a vacuum), you aim at 45° elevation; in other words, split kinetic energy evenly between vertical and lateral velocity. (I dimly remember having proven that, but am not awake enough to do it again now.)
It follows that the kinetic energy of a perfect vertical throw is twice the vertical kinetic energy of a perfect distance throw.
The arc of the latter is a parabola, of course, and its height is easily found to be a quarter of its length. Double that, because with double the energy you get double the altitude; and the result is consistent with Munroe’s estimate.
What about air resistance? The vertical throw has a moment of zero speed, but the distance throw’s minimum speed is 1/√2 the maximum; so it seems to me that the vertical throw suffers less air resistance (not even considering the thinner air up there), and therefore the altitude estimate given above is low.