I think that's the idea behind the difficulty. As global hashrate increases, the difficulty increases and the profitability of mining BTC begins to decrease because you need more hashrate to earn the same amount of BTC. This obviously costs USD in both mining hardware and power consumption. At some point it becomes unprofitable and miners shut off, and the difficulty drops again. There's really no evidence to suggest that miners shutting down would affect the price of Bitcoin negatively (assuming there are suffiicient miners to continue finding blocks), nor has the price of BTC really been correlated with the global hashrate, as far as I know (I can't back this up with any data atm).