Point being, trust and trust-worthiness are two separate things. Most people investing in Bitcoin have not in any way confirmed for themselves that the algorithm is trust-worthy, they just trust that others are also willing to buy it so that they won't be left defrauded. Hell, people have been defrauded by the likes of Mt Gox, and the network didn't collapse entirely.

But there's also the people that invest long-term because they think crypto currencies have a lot of potential to be adopted more widely in the future, which entirely depends on their trustworthiness. Without that second group, any sufficiently negative news would cause the BTC price to collapse completely -- and to be fair, there's always the risk of that happening (Tether sends its regards), but the underlying "trust in the benefits of the system itself" at least gives a floor for its price that's above $0.

Ethereum has done it this way: First you build a stable blockchain, secured through tremendous amounts of power. Then, once your system has been widely adopted and people have "skin in the game", you switch to Proof of Stake to minimize power consumption while still maintaining security.

PoS is the better solution, environmentally speaking, but it necessarily depends on there already being value in the system that people can be held accountable with and thus kept honest. But to reach that state, people have to trust your system first, and if you're not an already trusted entity, PoW is one way of achieving that initial phase of trust building.

I'm sure you don't want that though, because solar+batteries will power interplanetary civilizations somehow.