Depends on the usecase. Sites for local stores need opening hours. Having those information as plain html is enough but that can be extended via ajax to show if store is currently open... So no need for dynamically rendered pages serverside.
Having time/date wrong on your device - particularly a phone, which a lot of people use instead of a watch - is sufficiently annoying that it usually gets fixed.
Edit: Great advice! Works like a charm! I've never really worked with dates in JS. Should have read the docs earlier ;-)