Validating data from the client should always be done on the server in that context, regardless of if state is being saved client side or not. I think this is just an extension of what you said though.
I can think of many apps that don't need server side data storage or security that would benefit from this type of state saving however. For example, this app that I was using today - https://wheelofnames.com/ . Right now to save I need to create an account, presumably to tie my account to the saved state on the server side. That's pretty heavy/intrusive when all I want to do is keep the names list and preferences populated for my next visit.