Most people are answering the title question but is your question about why people use a VPS or paid server for a Lemmy instance instance of hosting at home?

Content is federated in. My home server is not a good place to keep unknown images, videos, and links to other content. The risks associated with hosting user content are the main reason for using a data centre instead of home hosting.

There are also other benefits like complete separation from my personal hosted services that are actually hosted from home, and privacy and security reasons. As an example, my home hosted services are not available from outside my country, which virtually eliminates the malicious vulnerability scanning bots that constantly hit the domain before I added that limitation. But you can't have that limitation for a federated service or it wouldn't be able to federate. I have this country restriction on my router as part of the port forwarding rules.

But mostly it's that first thing about the user generated content.