The reality is what youre asking for is very complex - you're asking for lagless streaming for a desktop. That is running a GUI on remote hardware, and then streaming that video to another computer with low latency so you have no perception of lag in moving the mouseor interaction, and continuous streaming of desktop updates.
There are lots of factors at play that can make it a poor experience.
You can have what you want if:
- The server you SSH in to has the resources to run X well
- The server you SSH in to has the hardware to be able to then convert that to video (with some tricks) and stream it
- The internet connection between you and the remote server is stable and high enough bandwidth to stream the desktop
- the internet connection between you and the remote desktop is low latency.
Its very hard to achieve all those things even when youre creating machines that are dedicated for remote desktop streaming. I have done that in my work with Windows devices and to get good quality streaming we needed dedicated hardware, dedicated software and high quality internet. And even then some of our users had bad experiences.
Most remote servers are definitely not set up to provide what you want. Dedicated software for the task will help as there are lits of tricks that they apply to make a streaming desktop appear latency free versus simpler solutions that just stream the actual desktop.
VNC is not a good solution - its basically just taking screenshots and streaming those to you. It works with fast devices on a local network, but is very limited in your use.
If you really want to solve this look at software optimised for low latency uses such as gaming. For example Moonlight/Sunshine are for game streaming but work with desktops. They are designed to be low latency high quality. But to achieve that you need the video hardware on your server, and the good low latency stable internet connection.
Real world high quality desktop streaming also needs good graphics hardware and optimised tools. It can be achieved with open source software but you need the hardware to to do the heavy lifting.