If you self-host your repository, you don't have a hosting provider. There is no-one to "pull the plug" on the server at my business's office except the people who work in the building who could literally pull the plug, and I suppose the electricity and phone companies and our ISP.

What you are talking about isn't self-hosting, it's hosting in the cloud on VMs you're renting directly. This is an intermediate step between self-hosting and using a fully hosted service like GitHub.

With cloud-hosting, you are probably still subject to the whims of your hosting service. For example, you might be subject to occasional forced restarts of a long-lived instance if your hosting service needs to restart or replace the underlying physical server.

However, in most cases, unless you're doing something illegal using their equipment or compromising their system in some way, these hosting services don't much care what you're running on your virtual box. This option is still far less risky than using a fully-hosted service, not least because you retain full control over the underlying data so there is almost nothing that can happen because of your hosting provider that a reasonable backup strategy can't fix within a relatively short amount of time.