To search your home, a warrant is needed. To search a remote site, less is needed, and you might never know it’s been searched, back-doored and compromised.
Mostly because the small satellite server requires very little storage, cpu, or memory. I have about 100G of mail on my IMAP server (not all in one account: I run email for everyone in my family), and that kind of space isn't cheap in the server rental business (despite the fact that a 2TB drive is $90).
Plus I just like having my data here, and not somewhere where I have no physical access.