I'd disagree with that for most messaging apps. If you think about Discord or Slack for example. You have a plain text message and then media attachments externally. This could be very well expressed with JSON.

Very few messaging apps let you go beyond plain text and let you start embedding media or complex layouts inside a message.

Slack messages contains a lot of additional formatting and media.

Even whatsapp does formatting, so does signal.

What is a current popular messaging app that does not have rich text features?

Slack messages have a ton of formatting. You could implement it with some sort of extension on markdown but you'd have to write a custom parser. XML gives you a markup structure for free.

Slack canvases have full layouts including images.