Gratuitous use of electricity is anti-economical regardless of the source.

Electricity has higher economic value due to miners seeking to maximize profits.

This makes investments in renewable energy infrastructure more profitable and paid off sooner. A solar farm has more demand and higher margin for its products.

On the other hand, it means cheap coal energy is also financially productive.

What is anti-economical is the unfair price competition due to externalities not captured by coal energy's pricing.

"gratuitous use" is completely subjective, so the anti-economical assertion isn't provable. You're suggesting there are no trade-offs between PoS and PoW, no tradeoffs between solar+batteries vs coal or nuclear.

Yes, I'm saying there are no trade-offs between PoS and PoW. If there's one I'd like to know what it is.

PoS can be easily copied and modified by the powerful. There's little cost to create the system and force adoption rather than incentivize. There's an enormous amount of investment and technology dedicated to bitcoin that makes it more resistant to devaluation and duplication. But it saves electricity. That's the trade-off.

Why not focus on the source of the electricity rather than what the electricity is used for?

I don't see how proof-of-waste makes bitcoin more resistant to devaluation and duplication. How would switching to proof-of-stake make bitcoin more prone to devaluation, for instance? As far as duplication is concerned, bitcoin is open-source software which means anyone can duplicate it and make derivative works from it. There are dozens of bitcoin clones. It doesn't seem that bitcoin is resistant to duplication at all, or that there is any reason the lack of difficulty with which it can be duplicated should be influenced by whether it uses proof-of-waste or proof-of-stake.

Any software engineer can clone Twitter. The value of it is in the network and the high cost of users switching because they can't convince the people they follow and those who follow them to switch at once. The same applies to Bitcoin, but miners have an even higher cost of switching because they have specialized hardware that can only generate revenue on the Bitcoin network. Ethereum validators have a much lower cost to switch.

> proof-of-waste

It's Proof of Work. Productive work has value and in this case, it's widely distributed censorship-resistant validation of transactions.

Network effects have to do with the amount of users, not with the choice between proof-of-waste and proof-of-stake.