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.
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.