I think one thing that is not being considered is that for most customers, branding and the consistency thereof are key indicators of trustworthiness - especially when dealing with financial information. HN users are rare creatures, they have technical context the average end user does not have. The rise of phishing has lead users to pay a great amount of attention to subtle hints of impropriety, like being taken from one sort of visual experience to a vastly different one. We saw vast improvement across all meaningful metrics when we switched from plain text to HTML emails that utilized branding consistent with our website.
As with everything that humans deal with, there are tradeoffs here. And I'm extremely concerned that this position taken to it's logical extreme would lead to the web being transformed into something that is "safer" but much less useful and dynamic. One outcome of this could be the slow death of the open web in favor of siloed networks and platforms serving actually functional content in "safe" ways.
You could maybe see banks having plaintext communication as an optional, but I doubt they'd make it default (allowing users to switch to html).
Isn't this problem already solved with certificates online? Shouldn't this be solvable the same way? E.g. a bank sends an email containing a link to the content with some special attribute. The web browser displays the content if and only if the sender domain of the email (e.g. hsbc.com) is also the domain from which the content will be downloaded.