Yes, but IMO the Matrix team should _really_ focus on Dendrite since Synapse is extremely resource hungry and prevents a lot of people (including me) from running their own servers.
It's not that resource hungry anymore. Hovering stably around 500M RSS and 8% CPU for me right now. That's with ~25 users and a lot of federated, public rooms, some of them quite large.
What CPU are you running it on and how many cores are being used? Are you also in really large rooms like Techlore and Matrix HQ? Because I think I'm in all of the largest rooms (and a lot of the smaller ones)
I'm running my instance with lots of bridges in a 3-core 4GB server, paying about eight euros a month for it. Synapse runs just fine, but I'll probably switch to the Rust impl when it's done.
If you want to go cheaper and have only 300-400 Mbps of bandwidth, I've heard lots of good things about this provider:
Contabo is great: finally a provider that does not save on mem and disk space. I moved everything to them and I save tons of money. The 400mbps is only for the cheapest as well: you can pay more to get more. Not that most people would need more. Especially for running matrix for a company etc.
Not those two (and I know those are especially large), but we are in many 5-10k rooms, including bridged Freenode rooms which are known to be some of the worst offenders.
Note that many significant improvements have landed very recently, for instance the chain cover stuff which significantly improves handling of rooms with frequent membership changes (such as the aforementioned bridged IRC rooms).
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.
The Matrix team is doing a LOT of cool stuff. :)