Miners solve for nonsense problems because that's the simplest kind that you could solve in order to make the proposition work, anything on top of that requires more complexity.

So it's not that it isn't possible, it's just that it would be charity from the point of view of the developers of the software to spend brain cycles on something they don't strictly speaking need to achieve their goals. I'm pretty sure that at some point there will be 'green' crypto currencies, let's call them 'greencoins' that make a play at avoiding the waste of energy that digital currencies are becoming associated with.

The same happened in other industries, I don't see why digital currencies would not be able to follow a similar path.