The author's point is that in his experience many designers fail to understand germane properties of real world components. For instance, designers of switched mode power supplies look for low forward voltage only and fail to understand other properties exhibited be real world components. Depending on the actual application environment, secondary effects, like recovery time, barrier charge, reverse current may become dominant. Therefore a real world Schottky diode may be a poor choice, in comparison to other diodes, with higher forward voltage.
Yes; in my experience, schottky can perform worse, in applications where the higher capacitance hurts worse than reverse recovery does; or in pulsed application, where the internal resistance is just too high, with results ranging from simply poor operation, to destruction.
So, snubbers may be contra-indicated, and perhaps some nonresonant converters.
That said, I've also had good results with a couple of snubbers using SiC schottky; they happened to have modest peak currents, and the added capacitance wasn't too troublesome.
I don't have much to comment on the article; I will note that, although it makes light of the foward/reverse tradeoff, I haven't seen many diodes, or applications, where reverse power dissipation was objectionable, or actually dominant.
At nominal maximum design temperature. Leakage goes up exponentially with temperature -- it can very quickly run away. This is the sneaky part that can be easy to miss. And it's more about thermal design, always a challenge to solve reliably.
Also interesting to note that, what passes for modern schottky, can be quite strange indeed -- in the high voltage range where innovation is still going on. Namely, 150-300V Si types. Some of these actually have reverse recovery, they are just much better behaved than PN types (short t_rr, low I_rr, little dependence on forward-bias duration* or temperature).
*Maybe not well known, another quirk of PN diodes: when forward biased briefly (forward-bias pulse widths t_p comparable to t_rr, say), charge storage in the junction is nonuniform, and this is reflected in turn by the high transient Vf (forward recovery), and the shorter, uneven, and potentially
extremely sharp, recovery.
On a side note: I regret that I never met Walter Schottky, he is buried not far from were I live.
Well, if you can get the plot beside him, perhaps you can always make it a buried junction.

Or wait, I suppose that joke works better for his wife (er, if he was married--?).
Tim