Coinhive vs Recaptcha?

I'm not looking at the bad elements of coinhive – which wreck user's computers, and don't make publishers as much money as advertising, instead I'm looking at the better elements of coinhive – namely the captcha. 

The main advantage to it is that it pays publishers, as opposed to google. But it has other advantages: 

1. You could set up a mine-wall for premium content. If you set it up in a way that you show the publisher how much money you're making them users would likely understand how little money they make – and could be encouraged to make a donation (I recommend freewallet.org for that, as you can set up a page where users can send coins to one of tens of currency wallets). 
2. Hackers will be paying you if they try to brute force your website. 
3. DDoS attacks can actually make you money, if you force the hackers to mine in order to visit your site. You'd have to set this up with redirection (redirects to your site).