Very relevant for heavy users. I regularly find Chrome unusably slow (Firefox handles heavy usage much better), so it's good to see that Google are at least acknowledging the deficiency and working on it. I has little to do with network speed - a modern browser is practically a crude OS, so things JavaScript speed etc., rendering/layout speed, memory usage absolutely matter. Secondly, these browsers must run on relatively low-end devices e.g. low-end smartphones.