No.

1) Many hosters provide OS templates including popular ones like Proxmox.

2) Usually you can install any OS by providing an ISO, sometimes doing it via KVM remote access.

I'll add many have remote access that is like a serial port. Digital Ocean has a "recovery console" that appears to work in a similar way. It runs in your browser. It works when other stuff breaks.

Now, for Linux, they have a SSH client in the browser enabled by default. I use it to manage a pile of $5/mo droplets, like the author.