I don't know about Tuta specifically, but Protonmail is practically intentionally hostile against anyone using their own keys. Which is the biggest sign that their marketing and actual intent do not align.
So it "breaks end to end encryption" even with smtps and imaps apparently. The few emails I received weren't from tutamail users so presumably came over SMTP.
It's confusing to know what they mean because they confuse terms. They say emails are "stored end to end encrypted".
They don't pass my smell test
Did they say what's stopping them from using that (and requiring the encryption!)?
How would the lack of IMAP compromise encryption? Sounds dubious.
Lock-in effects are problematic, but separate from encryption or privacy in general.
If the concern is actually lock-in, it is worth noting: there is little lock-in in the current Tuta offering. The service allows users to export emails into standard EML files. If you decide to switch providers, simply point your domain to the new provider and import your latest backup.