The federation is chatting around the clock. Remember, joining a Matrix room means that your server needs to handle all of the room's traffic. And 25 users can easily be in a lot of large rooms. However, each room only needs to be handled once, so if more of my users join a room in which my server is already participating, the cost doesn't increase.

That said, this isn't an average but a spot value. It frequently falls below 8% (though typically stays above 5%). Note that this is a cheap and relatively weak VPS.

I'm not saying Matrix is terribly lightweight. I'm saying you can easily run a small personal instance on a cheap machine without any performance problems.

If I run Weechat on my VPS, and join a few high-traffic IRC rooms, I expect my average CPU use to be 0%. Same if I run mailman with a few messages per minute, or an IRC server.

The fact that we can now run it on a VPS is an improvement, but it is still orders of magnitude heavier than equivalent non-decentralized systems.