If there was a way to verify the power source is green I think PoW would be the ideal way to move forward. For example if electrons generated by photoelectric cells somehow were different than other electrons (quantum spin, parity, etc.) then maybe an algorithm could check for that and only accept blocks mined using these electrons and not others.
Any crypto system that has an energy problem also has an economic problem. When a transaction requires the same amount of electricity as an average household uses in a month, then each transaction will cost someone a full months electric bill. That will either have to be paid with extremely high transaction fees or "absorbed" by the value of the currency in ways that make it unsuitable as an actual currency.
This is true regardless of the environmental impacts of the specific energy source, and while solar and wind are decreasing in price, it is unlikely costs will drop so much to make this issue negligible.
Currently transaction fees are so high because of bitcoin block subsidies once the subsidy asymptotically approaches zero there will be much lower transaction fees because miners only incentive will come from the fees.
There are far too many blocks being mined not because of volume of transactions that need to be included in them, but because of new block subsidies.
