Actually I wouldn't mind if Reddit were start to cache some things client-side. For example their voting is eventually-consistent, which means that my votes will be eventually saved by not always immediately. Because of this property (consistency) it would be save to remember cast votes on client (local storage or cookies, though the latter might not be such a good idea with all this 408s I'm seeing right now) and so it could spare me getting angry when after refreshing page or navigating to another view all my votes seem to be lost.

EDIT: Though on your point I don't see how doing anything else client-side can help Reddit with scaling.