That does not seem like much of an assumption; all modern mail clients that I am aware of do this.

The problem isn't the clients, it's the senders. And as someone who uses Mutt, the vast majority of HTML emails don't have usable plaintext versions.

What kind of mail client doesn't send mail? I am talking about someone using a mail client to draft and send an email.

Sorry, I realised that's what you were talking about after the edit window closed. Though, a lot of mail is sent by mailing services not individual clients (and all the awful ones really don't like sending useful plaintext mail).

Hahaha, that's rich. Those laws are not enforced. I actually consulted with a blind friend when writing that up and he agrees that every HTML email is a nightmare for him. Top posting too.

However, a significant portion of HTML mail I receive happily violates "accessibility laws" and omit to provide a text-only part. I know that, since I actually rely on accessibility to do my daily work.

To clarify, is your problem with HTML emails that omit a text/plain part, or only HTML emails that have images with no alt text? If the latter, I think the solution is to advocate for accessibility in HTML emails, not plain-text emails. After all, well-structured hypertext has its own accessibility benefits, since most current screen readers have lots of commands for navigating that structure. This is why I disagree with advocating for plain-text email in the name of accessibility, as this campaign does.

Screen readers should be able to deal with HTML-only mails for the most part, otherwise you should send the sender of that mail a reminder about those laws.

Are you actually a user of accessibility? To me, it doesn't feel like you are. If I am right, please refrain from patronizing people who actually do. In my book, you have no idea how horrible the situation has become over the last 5 to 10 years. Accessibility used to be a thing, yes. These days, it is mostly a happy accident.

I've never talked to anyone who actually used accessibility tools. I'm aware of the W3C standards. Are there any other resources that developers can use to produce stuff that works well with real-world accessibility software?

Yes. Real-world accessibility software.

How do they manage to do that? Embed the text as an image?

Basically you send two versions of the mail any one who has sent mail programmatically will have dealt with this.