It's not very common but that concept already exists. You can rent out computing power through some companies. Or 'donate' it to science it for things like protein folding or astro analysis.
Of course you're still paying for electricity, which is often the problem: you don't want your phone to drain five times as fast when you're not using it, and you don't want to net lose money on electricity bills while mining bitcoins.
I think one interesting consideration here is how much of the costs are actually the hardware, and what you save by running it on people's personal computers. Power and labour are other costs.
By running your calculations on unknown hardware, you introduce reliability, privacy and intellectual property challenges. Is that worth it? For scientific data from space it's probably okay, but a bank or national tax service would hopefully think twice.
There is a field of security that studies this: you encrypt the input, run computations on it, and then you can decrypt the output and get the answer. But of course this isn't true for most encryption schemes (or all computations?), and I don't know much about it.