It didn't "win", it just happens to be in vogue right now, given the current economics of bandwidth and processing power. Give it another few years and some bright spark will start enthusing about whatever the next iteration of thin clients will be, and there will be a flood of articles evangelizing about how great it is to do everything on the server instead of putting up with all this complicated client-side crap, and oh boy doesn't the future of ultra-lightweight devices talking over reliable, high-bandwidth links to big central servers sound awesome?
Such is the ebb and flow of networked computing.