So cookies can be used in a secure way but most existing code is a bit buggy and while IE and FF can be totally safe some of the small fry aren't up to speed on fixing some potential cross site scripting holes.
And the proposed solution would require getting 100% of clients upgraded to a browser version that doesn't currently exist. How many hits does the average site still get from IE6? Typical security researcher living in an academic nonreality proposing improbably solutions to things that aren't even serious problems in the real world.