>the only time you know it's not the same thing is if you go offline or have bad connectivity.
So, like most of the non-first world? Hell, I'm in a smaller town/village next to my capital city for a month and internet connection is unreliable.
Having said that, the website was usable for me - I wouldn't say it's noticeably fast, but it was not show either.
I feel like it depends a lot on what kind of website you're using. Note taking app? Definitely should work offline. CRUD interface? You already need to be constantly online, since every operation needs to talk to the server.