How much of this performance do we actually utilise?

Depends on what you do. I compile a lot of stuff and do 3D simulations, so I am in need of all the power I can get, and I utilize everything my computer has to offer.

wasting all that compute power

I wouldn't say having a powerful device means utilizing it 100% all the time. Especially consumer devices are not built for that. It's more about having the power when we need it. And that's not wasteful imho.

What if there was a way to provide our devices' compute power to someone more in need.

There are ways, like SETI@home (since 1999), which allows others to use your compute power when you don't need it.

What if we could rent only our compute power to someone?

Who would rent it? Companies usually have the money for much better specialized hardware and comput-farms, which provide more power with faster latency. Most home users just use one of the big cloud players, like Azure, Amazon or Google, because they are cheap and offer so many other features. You'd have to create a platform with many players and features to get anyone interested in your computer.

How feasible is this?

Quite difficult. Getting people on board, managing contracts, payments, laws, that stuff is expensive and complicated. Plus you'd have to find a way to package workloads, so that they can be sent to any computer, be computed on their own, and then get the result back. This process would have to be a lot more performant than just calculating the problem locally in the first place. Which reduces the number of problems one can use for this kind of distributed network. You'd have to specialize on certain problems, find companies which have these problems and then hope that they are willing to use your service, because they usually have their own equipment and probably also don't want to send their data to a foreign network of computers they cannot control.

What are its security implications?

You need to make sure that all participants are cleared for the kind of data they process. And sometimes there are secrets, which should be kept. By contract. Again, lots of work for not a lot of money for your average Joe.

Would we be okay to increase our energy usage (and consequently our carbon footprint) just for a little rent money?

I doubt the turnover would be anywhere near enough for your rent. Compute power today is very cheap, because all the devices are so powerful.

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.