I grew up when there were still steam locomotives hauling Britain's express trains, and later on, my first dial up email was, I think 4800 bps, soon followed by 14400, so excuse me a slightly backward outlook.
I habitually use plain text for most things. Out of the wonders that technology has given us, I believe that preserving HTML code when making inline responses must surely rank very low. The complexity of preserving what could be quite complex and completely arbitrary markup across an inserted inline comment must be considerable. Is it worth it?
BUT...
I can think of one small justification in the text domain for keeping it, and that is in lists, for example bullet points.
In my mind, though, this still ranks below images.
Even so, I still personally prefer NOT to embed images in the text if my use is personal. I use attachments instead. I can see that a business may want to have logos, 'signatures' and brand images embedded in emails, but as soon as I want to make an in line comment in my reply, the need for the embedded structure (as opposed to content) to be preserved reduces somewhat.
From a business viewpoint, too, if you do value the structure, the integrity of the original is still lost by inserting comments inline.
Every email client I use seems to work backwards in this respect anyway. You can either insert comments inline and optionally delete parts you do NOT want (itself a great reason not to try to preserve HTML, as you mess up the tags). Or, you quote the whole thing.
I am always looking for a split screen method that would allow you to pick up one by one, sentences or sections you DO wish to reply to, with an automatic: "you wrote:" in front of each abstract. Nobody does this, so I guess I am living in the wrong universe.
I recently had to deal with two solicitors (uk - england and wales - speak for lawyers serving the public directly) in the space of a few years on similar topics. One would accept and send emails at a lower cost (for a short email) than for a letter, and she used only plain text. (Only once did she send me something as an attachment, and that was a form I had to print and sign. Sadly, here in the uk, sending a form this way is as rare as hens teeth, as a single company [OYEZ] has copyrighted almost every official form an English solicitor needs to use that are not already Crown Copyright, and only originals are accepted). Legal information about the company and standard disclaimers were in plain text signature blocks. The other sent very brief 'covering' emails with PDF attachments. The attachments were identical to a paper letter on headed paper, and she charged the same as for sending the letter by post.
I found both of these approaches entirely satisfactory from a business viewpoint, and clearly so did they. I believe the second solicitor was living in the past a bit, and just protecting her income by not embracing the flexibility and speed of email, but if a lawyer can conduct business with plain text emails as the first did, so can anyone.
My heart sinks when I receive a personal email with an embedded image of about 25 megabytes that has neither been compressed nor resized, and shows only as a corner of an image that is about A2 size, that I then have to save and open in an editing program!