Total control. Let’s take the budgeting app for example. I started using Mint in 2009. There’s more than a decade worth of banking, spending, and investment information in there.
Mint is shuttering in about a month. They gave all their users a month and a half notice. When it’s gone, it’s gone.
When a self hosted app is used (with appropriate backups, orchestration, etc) YOU the user get to decide when you’re done.
If something isn’t working for your life anymore, you can find an alternative and migrate everything over on your own schedule.