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 cancer cure anyway. The incentive of a block reward (within the currency) is not primary. Thus there is diminished incentive for the network to create a linear blockchain, where everybody mines on the most recent block. Without that, you cannot order transactions.
A cure-cancer PoW where each block fixes all of cancer is ridiculous.
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.
Except the miners don't gain value from discovering a protein fit, so they have no incentive to mine the wrong chain.
Even then, as long as the coin value is larger you will have a consensus with the miners to to mine the latest block. Any sidechains will be neglected, which is why this "no value or nothing" attitude doesn't fit a blockchain network.
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 cancer cure anyway. The incentive of a block reward (within the currency) is not primary. Thus there is diminished incentive for the network to create a linear blockchain, where everybody mines on the most recent block. Without that, you cannot order transactions.