Re: alternative to micropayments?
"you know, if it was clearly announced, secure, and reasonably throttled, why not let mining happen to support a site you like?"
Because it won't actually support the site; income from web mining is tiny compared to adverts. And that's when it's all working as intended. Throw in constant price fluctuations so you have no idea what your income will actually be in a given month, and the very real possibility that the pretend-coin you've opted for will simply disappear overnight (Bitcoin is hardly stable, and that's by far the biggest and most reliable one around, other pretend-coins keep popping up and vanishing again in their hundreds so good luck guessing which will still be around a few years from now), and it's hardly a sensible looking business model.
And even if the one you pick does happen to be around in a few years, how will you mine it then? There's a reason no-one is using Coinhive for Bitcoin - you simply can't mine it using spare cycles in normal home PCs. Pretty much all pretend-coins have a similar mining difficulty curve, they just haven't been around long enough, and aren't popular enough, to have hit the same level. If browser mining ever became popular, it would very quickly make itself obsolete.
"beats paying $60/year or the like for Washington Post."
Does it? Have you actually calculated how much you'd pay in electricity costs to support a site this way? And importantly, have you calculated how much income you'd actually generate for them in doing so? It's far from trivial to turn a profit from coin mining. It's extremely likely that both you and the site you want to support would be better off if you just paid them some real money instead of going through a convoluted Rube Goldberg scheme to turn that money into virtual commodities via your electricity bill.