I have no idea, I have zero desire to host a matrix server. But I wanted to have one, I would make sure to check what the actual requirements in terms of bandwidth and storage are and what will happen if I fire up the server.
It's like hosting a TOR exit node and then complaining about all the data going over my network.
You do understand that running a federated server means that you are taking over hosting duties for that chat protocol, right? I wonder, why do you want to run a federation outpost if the requirements to do that seem annoying to you? Just join the group via matrix.org's own server and you are settled, they have the knowledge and the resources to run a proper matrix server.
Edit "a single group" with maybe hundred thousands of cat gifs takes a while to sync unless you instruct your server to omit the backlog.
Depending on your config, joining a large group means syncing backlogs of weeks/months/years of posted media, so what do you expect?
I just say you seem extremely uninformed for somebody who want to run a federation outpost, i.e. from the FAQ: https://matrix.org/docs/older/faq/
Why is the state_groups_state table so large? What is it storing? Room state takes up a lot of space! To be specific, regular snapshots are taken of room states, so you can rapidly find out the state for historical events.
Why is it so important to record this, and to know the past room state including full member list?
It's needed to enable access control and state resolution, for example the homeserver needs to be able to decide:
"who can see this message at that point in time?" "what was the state of the room was when this message was received, and so is it allowed to be received?" Synapse stores these snapshots approximately every 100 messages, with deltas in between.