There is a relation though, although admittedly it's the other way around: the more expensive bitcoins are the most money can be invested into the mining proces

There is a relation though, although admittedly it's the other way around: the more expensive bitcoins are the most money can be invested into the mining process which correlates strongly with the total amount of energy "wasted" mining it. If BTC was worth $4 the hash rate would probably be a tiny fraction of what it is today.