If "difficulty drops, costs go down" so ought the price? Isn't that basic economics? Or are they chasing the "phase difference", lag, between supply demand?
Bitcoin's supply won't increase as costs go down, unlike other assets.
Um. That's a causative relationship, even if it's mediated, but it's still causative. And generally, the relationship is even more direct: the suppliers are quite reluctant to sell at the price lower than their costs unless they expect the prices go up soon enough™, so the lower boundaries for the prices exist.
Competing for it is more of a game that has a cost to participate in.
As price per coin goes up, more folks will find mining profitable and invest in mining operations. Difficulty goes up until it's no longer attractive for anyone to add to the global hash rate.
As price per coin goes down, less of those operations are profitable and fewer new people will find it to be a good investment. Difficulty stays the same or goes down. Due to capital expenses, difficulty is more sticky in the downward direction than upwards.
There is of course some marginal price action in between where there is in theory selling pressure from miners when it's less profitable to mine (to fund operational expenses and debt), but I don't think it's super material to the overall market volume these days.