I think this idea has some serious flaws. In fact, I believe the project will fail because people don't want their CPUs being used for mining. Period. They don't want adds, but they want to mine Cryptos for someone else even less. Just look at the recent headlines about crypto-currency mining adds. I know they aren't the same. However, when people hear about this, they are going to equate it with the same thing. If it ever makes it mainstream, their will be major backlash.
I think it will be the opposite. There might be some short term public outrage, but after the 24hr news cycle moves on to something new then everyone will forget about it. The only ones who really pay attention will be people like us, which makes up a very small percent of total internet users.
Hopefully. However, I wouldn't even be surprised if crypto-mining on user's laptops was banned via a law. It's something I definitely could see happening. At the very least, they are probably going to be forced to put up a banner asking user's permission to do it (similar to the cookie banner that shows up on a lot of sites now). I am not saying I want this to happen (I would like PRL to succeed)-I am just being realistic.