You don't need to self-host, you can register an own domain and associate it with Simple Login. You would still need to re-create your aliases with the new domain but are free to change services any time onwards (assuming they allow you to bring your own domain as well).
It all reads harder than it basically is, just try it out and if it doesn't work for you, you can still use the default Simple Login domain instead :)
Here's the official documentation: https://simplelogin.io/docs/custom-domain/add-domain/
Not sure what the hardest was for me but Scarlet/Violet have by far been the easiest for me. There was literally no challenge at all.