How about a virtual machine? E.g. kvm, virtualbox, or similar?
I imagine you're suggesting something like X over SSH, right? Do you use something similar on a daily basis? I would probably commit sudoku if I had to use the entire VM (not headless).
Even VNC clients sharing clipboard content with the host system poses an attack vector, for example.
Of course this does not mean doing all of the browsing within the same vm, multiple vms for different things (banking, development, internet radio with flash, ...) after all RAM at least on the desktop is still fairly cheaply available, and on laptops one can still run a few browsing vms in 16gb if the need arises.