You'll be thrilled to know this pretty much isn't true anymore, even with Synapse. My instance is running on a cheap Hetzner VPS with a not very powerful CPU and is currently using about 700M RSS and not much CPU. And I'm in a lot of rooms, some of them quite large and high in traffic.

I'm also not even using Synapse workers at all, just a monolithic instance. Splitting the setup into workers would buy me an additional speedup if things got overly slow.

Yes, unfortunately Synapse is possibly one of the worst apps i've ever sysadmin'd for, and I'm not even the primary sysadmin for my homeserver. I still use it, regularly, but we're all really anxiously anticipating the release of Dendrite. I'm not the biggest fan of the protocol either, or the UI/UX of Riot. I think Matrix is a good idea, but there's a lot of historical baggage and I think the world probably needs one more "throw everything away but learn the lessons of the past" cycle before we get something really, truly good in the chat space.

Why does it require that much? I run a Jabber server, and it barely uses any resources on my VPS. Unless you mean for significant users?

If you want to actually use the federating feature, you will probably join some big channels. And that causes pulling of some huge amount of data from other homeservers.

disclaimer: I tested it some time ago with Synapse. Now I see there is also new homeserver software, Dendrite. It is possible that it is order of magnitude less resource hungry, though I wouldn't count on that.

One of our primary goals on the Synapse last quarter was to make it possible for a new homeserver to join Matrix HQ (a large, public room) in under 1 GB of RAM. And we did it. https://matrix.org/blog/2021/06/15/synapse-1-36-0-released

It's not the slimmest beast, in part because Synapse needs to scale up to country-scale deployments, but its ability to scale down has significantly improved over the past year.

That said, Dendrite and Conduit (https://gitlab.com/famedly/conduit/) are exciting projects which will optimize for different operational contexts.

How and why is that different from a client being in the room? I'm pretty sure that neither desktop, nor especially phone clients are supposed to take gigabytes of mem to listen to chats.

I'm not sure when you last tested, but my Synapse instance (v1.42) is currently using around 180MB RSS. I'm on a few rooms with 500+ users and multiple with 50+ users.