Earlier quoted context omitted.
I'm not sure I follow what you mean. I didn't mean that this be used for mining bitcoin, but rather that there are other cryptocurrencies that have useful by-products. Am I misunderstanding your comment?
These other cryptocurrencies are less secure than bitcoin. For them, the cost of attacking the network by mining on an orphaned chain is lower, because by definition the PoW has a useful by-product. The more useful the byproduct, the less secure the coin. Edit: to illustrate, imagine a PoW that computes cures for cancer. Somebody can now mine on whichever block of the chain he wants forever, since he's producing a ca…
A more apt analogy would be that each block would solve a protein folding or active site matching problem for cancer. Then each solution would be public, and useless to mine over again.