@Tutanota
> would be stored unencrypted in the third party email client.
In a browser, the email is stored unencrypted in a third party software, to be displayed. An email needs to be unencrypted to be displayed.
Having unencrypted data client-side is not the end of the world.
A third party email client is not the end of the world.
People use operating systems, browsers, hardware that are between them and Tutanota. Most people can trust these things, most people wouldn't care about minimal risks on their own computers regarding IMAP. Most people don't care if on their own computer data is stored unencrypted, it's not a risk if they're competent.
People want IMAP because they want to export email (unencrypted, doesn't matter if you think it's a risk, people can encrypt them themselves if they want). They want to remove their emails from the cloud, they want to have access to those emails once they delete their Tutanota account years from now.
Offline availability is temporary, exporting mail in a standard format is the real solution.
If you don't want to use IMAP, you might develop a new, secure, free, open source protocol, then develop a free, open source extension to Thunderbird, K-9 Mail, and some other clients.