If I answer you no then I'll be lying. Even though my hope is for us to see 1 btc equivalent to 1 btc some day with the price of fiat mean nothing to us, the current movement of the price still gives us the indication in how well accepted btc is and its demand. I do agree with your reasoning but until the I will still closely follow the btc price movement.
That would be definitely lying. Ofcourse the price always matters that's why some people began to be interested to use bitcoin to have a source of income. Many people would definitely leave in bitcoin if the price of bitcoin will totally crash because all of their money will be gone including mine.