While you are entirely correct about the "no internet access" issue with IMAP in theory, but because that was recognized pretty early on it's been cured, for the most part in practice. Most e-mail client programs allow you to specify some set time period, working back from the present, for which to download not only the IMAP message headers but the message bodies as well for offline use. You can even do this in Gmail's webmail interface so that you have access on your machine if you don't have an internet connection.
If one knows one is going to need offline access, either for a given one-off time away from internet connectivity or on a regular basis, tweaking the client setting to download the bodies for the messages one is likely to need should be done.
Brian - Windows 10 Home, 64-Bit, Version 1709, Build 16299 (dot level on request - it changes too often to keep in signature)
The opposite of a correct statement is a false statement. But the opposite of a profound truth may well be another profound truth.
~ Niels Bohr