What is the difference between making sure an HTTPs endpoint does not leak and making sure an IMAPs endpoint does not leak? I do not see much of a fundamental difference.
Except, it makes the user experience worse: I can certainly make it infinitely more tedious to open the document exchange site of $superimportantcompany on superimportantcompany.co (or was it .com? or .co.uk? or important-company-le.ai?), and spread out "my" inbox across 30 different sites and spend additional time navigating their unique interfaces to not just read, but also add each document into the appropriate local archive. But what have I gained in making it more likely that each correspondence is kept confidential between the only parties that should read it? Nothing beyond what I started with. Could have stayed with email, no?
I can see the appeal of mitigating part of the usability problem by pivoting straight to bundling up all thematically related messages into centralized repositories to limit the number of pseudo-mailboxes one has to maintain simultaneously, as done in the recent "everything medical related" cases. But someone would grab a full copy in the inevitable compromise, and that is a risk that should rather stay scoped to smaller groups of senders and/or recipients. It seems like a bad tradeoff to force every blood test of everyone into the danger zone for that, given that one could have instead spent 3% of the budget on.. merely policing away the DNS warts in public authorities (or, in the medical example, insurance companies) while keeping data custody unchanged.