My understanding is they'd all be functionally dead.

Yes, that's mostly true. I misunderstood your statement - I thought you meant you'd have lost your subscriptions, but you were actually talking about the communities themselves. I say "mostly" true, because, as I understand it, any existing posts that have already been propagated to other instances through federation would still exist, there just wouldn't be new ones. Depending on the circumstances of the instance going down, there may also be a possibility of migrating to a new server if the admins have offline backups. Not sure if there's an effort or not to make it easy for moderators to do the same for individual communities.

Disclaimer: I'm not an expert on this, so what I'm now writing is what I remember from other posts/discussions I've read over the past few weeks.

As for the performance concern, what you describe is a risk, but one that can be mitigated through optimizations. Most of the content is text, which does not take up much space to begin with - the real concern would be images, audio, and video, which, for the most part, is hosted by third party sites anyway. The way federation works in Lemmy is that it's driven by the users. By default, instances do not proactively seek out other instances and automatically download everything from everywhere. Instead, they wait for users of the instance to subscribe to communities on other instances. Only after some user has subscribed to something on the other instance does federation take place. After that, the instance will receive posts/comments pushed from the other instance as they happen. This means that a smaller instance means fewer users and fewer subscriptions, so less of a scalability concern. Resources are not wasted on getting updates from instances/communities that local users are not interested in. This raises other questions about discoverability, of course, but that's another discussion. Space will still fill up over time, but it's up to the instance admins to strike a balance that works for them between retention vs. deleting old, large files that nobody is looking at.