This is actually tricky for performance reasons. Lowering priority, please raise back up if this is important or becomes important later.

For future reference: it's possible, but care must be taken when tables are too large. Knockout (the framework we used to build this) is not actively maintained and we'd have to write some custom code.
It seems this binding is a good place to start:

https://github.com/apuchkov/knockout-orderable (live example: http://apuchkov.com/knockout-orderable/examples/basic.html)

The tricky part is that our tables are rendered with a custom binding instead of a plain foreach. This is to support super long tables. These shouldn't really exist and we should paginate, and that's where this starts getting complicated.