I believe the proof-of-work calculations automatically become more difficult as more computing power is dedicated to solving them. The net result is that the amount of energy consumed will probably increase inversely proportionally to any reduction in power prices.

Will the concept of money still mater as much if at all if all energy is free?

Let me rephrase - “will anything be scarce if electrity is free?”

The answer to that is obvious: yes. So why wouldn’t we need money?

Agreed, hence "as much". My thoughts were that the main cost of 'stuff' is the energy used in mining or preparing it. If you have free (cheaper) electricity, you don't need oil, metal production has it's biggest cost removed, etc.

Variable costs are eliminated so the amortized fixed cost of hardware is the only ingredient for price.

Basically the price (demand) for hardware goes up and should equilibriate when it reaches the previous cost of energy.