Those images are effectively attachments that are referenced in the markup of the HTML. You can still view them just fine as attachment in mutt.
Sure it can be cumbersome if the various images are interleaved with commentary, but in my experience 99% of the time it's "Here are the pictures/documents you wanted" followed by a few attachments (inline or not).
There's a very, very small proportion of emails where HTML is actually mandatory to make sense of the contents. And for those I can just tell mutt to load the HTML in my web browser. I very seldom have to do that though, not enough to be a real nuisance.
Email clients like gmail/outlook put images in the content of the email (NOT an attachment) when you drag/drop files onto the window or when you copy/paste a picture inside the mail.
There was a time when this all went to attachment, that is not the case anymore.