No one has complained that gold mining wasted too much energy, since that is a must. You must overcome certain natural energy barrier to mine gold, there is no other way.This energy requirement is fixed regardless of gold's price

However, for cryptocurrency, you don't need to overcome a fixed natural energy barrier to get bitcoin. The only barrier of getting bitcoin comes from competition, it is other people that created an energy barrier for you to successfully mine bitcoin. And this energy barrier changes depends on coin value. During early days of mining, the barrier was very low

Given it is a barrier generated from competition, the competition model can also be designed so that it takes other type of energy input. Besides electricity, is there any other energy input that is more efficient?

Since fiat money can be regarded as universal form of energy (it can exchange any kind of energy source like petroleum, coal, nuclear material, etc...). By design a competition model based purely on money itself, like bidding, it will achieve the same effect but without any waste: You win the bid, you get new coin, if you lose the bid, you lose nothing. While in traditional competition model, the one who lose the competition also wasted lots of energy