I think btc price is not directly correlated with difficult, is the opposite.
Difficult needs to adjust to btc price, because less efficient miners need to shutdown their equipments.
So you are basically saying that as Bitcoins get more expensive, difficulty needs to go up? And because of the difficulty increase miners need to stop? So as Bitcoins get more expensive, people need to stop mining? Your point isn't exactly well thought out. Even if GPU miners aren't making profit, their mining does help the network.
There's more than one effect IYAM, and that's definitely one of them. I think a network with a 250 million difficulty is more valuable than a network with 1 million difficulty, that too makes the coins on the network more valuable.
That is also a good point as well. So difficulty does in some way affect price.