rendering html obviously takes some resources now every user visiting you site is doing this. also not only rendering major logics are now done client side instead of server side.
date time issues - i just give the client utc time is a pre set format and done even care about the time zones i let javascript handle it. this is great advantage to where i had to guess time zones based on location derived from users IP.
to me state is more nicely maintained in an SPA because once you have set a variable you know it will be there. this gives a feel of developing an app rather than a web page. this helps a lot typically in making sites like foodpanda, flipkart, amazon. because if you are not using client side state you are using expensive sessions.
websites surely are extremely responsive - ill take an extreme example for this try making a calculator in a non SPA website(i know its weird).