From what I can tell, this is the sole benefit - in principle - of a random number generator. If you assume an adversary who can predict a deterministic world better than you can, then you can remove most of that adversary's advantage by making the world unpredictable.

But that's a very far cry from what this article is pushing. Randomness in this case is not making any system work better as the article discusses early on (and incorrectly hints at in some of the examples). Randomness is just a blind woman shutting off her lights in order to hinder a sighted man trying to harm her.

This is getting rather off-topic from the article, but I think you're making a stronger and more interesting claim than you realize. If randomness doesn't help algorithms in general, then BPP (the class of languages decidable in polynomial time by randomized algorithms with bounded error, more or less) is in P or some other deterministic class, depending on exactly how you define randomness not helping. There's all kinds of interesting research here.

As a concrete example, primality testing has been known to be very efficiently solvable with a randomized algorithm for a long time, but it was only recently that a deterministic polynomial-time algorithm was found. That algorithm is considerably more complicated than the randomized algorithms.

See http://www.math.ias.edu/~avi/BOOKS/rand.pdf for some more detail. I think there's a lot more research on the topic that I haven't managed to dig up in three minutes of searching.

Edit: another use of randomness: expander graphs are quite useful in a number of contexts. There are easy random constructions that provably produce expanders with high probability, but I'm not sure whether anyone has found a deterministic contruction that produces an expander.