Gas price doesn't have a real "going rate" like ETH does. Looking at http://ethgasstation.info/, There's 13% of blocks right now being mined by pools that accept 0 gwei for gas price, so it's totally possible to make transfers without paying any fees at all. The difference is that you may have to wait a bit longer for your transaction to be included in a block (because you only have a 13% chance that a pool who accepts your transaction will mine it).

Also, gas fees are very small. The median gas fee is about $0.26, which is actually quite high right now for Ethereum (in part due to the difficulty bomb before Metropolis).

If there was more competition over price, and if the prices were significant for people to actually profit, then gas fees might become more aligned with the ETH price. I'd rather have it be separate though.