Proof of work generates not as much wasteful byproducts, but far more relative to its current utility. Not its potential or idealized utility, but for what it gives now.
The cost-benefit on those two examples are at vastly different sides of the spectrum.
And your argument that because of that, we can't take claims about proof of work seriously doesn't hold muster. We can still do things about it. Just like we can still do something about the fountains at the Kardashian homes just being fresh running water (they were annoyed about the cleaning process, so had the bright idea to just install a drain and have the fountains be an open tap, so one of their homes was using 1/2 million gallons a month of water).
Ironically, to you, that's a drop in the ocean and we should let them do it because it doesn't move the needle.