For a while I was running KMail which is the default mail client with Debian KDE. It works quite nicely.
Many messages, at least the ones I see in my inbox, have an html component. By default, KMail tries to render all messages as text. At the bottom of the message window, it is possibly to show mail message body parts: typically there is a text component, possibly with one or more html parts. The html part can be clicked on to show the html rendering. If that becomes too unwieldly, it is possible to change a setting to use html view when ever possible. Remote content can be retrieved on an on-demand basis, but I don't think is 'remembered' on a by-sender basis.
KMail does have an offline/online mode where the content of all messages are saved locally. But it seems as though it retrieves a significant amount of content on each resync/refresh, and takes up considerable bandwidth when doing so. I didn't do any research into that.
Instead, I installed Thunderbird to see what it was like. I had two crashes while getting it started (during the initial sync processes), but now things seem to have stabilized. Once the initial syncs are complete, I'll see how much it takes to resync.
By default, Thunderbird will render html content as html content. And by default, it will not download remote content. When remote content is desired, it has an impressive mechanism for selecting which content to download. Better than even Outlook. It is possible to see from where the content is sourced. I have been turning on remote loads from sites which use similar names to the source of the email. Generic CDN (Content Distribution Networks) I keep turned off. These settings seem to be maintained on a per-site basis.
The nifty bit is that when replying to Outlook generated HTML messages, it knows how to 'break-in' to and perform inline text on the reply parts. Something Outlook can't or refuses to do.
There have been various rumblings that Thunderbird may become deprecated. Be that as it may, it still seems superior to some other mail readers, and is my new current email reader.
Any suggestions for other email readers?
Hacker News recently had an item on a Thunderbird Rewrite, but I don't think much consensus was reached. I was hoping to find suitable links to related solutions, but didn't find much of that either.
2018/05/22 - Mailspring might be worthy of evaluation.