The advantage is that the monitor provides the sort of usage data the company can sell to others. To be clear, it's not an advantage to you.

Could you give some concrete examples of the types of data that an existing smart monitor (not a TV) collects and sells to others? (Ideally also naming the manufacture and the device.)

Five years ago when I last looked into it, a "smart monitor" was a monitor running a custom Android setup that could do whatever a smart TV or tablet could do. The possibilities for data collection are practically unlimited, and recent experiences with smart TV updates putting ads where no ads were before show that potential matters; it's on the basis of potential that I'm against it, not because I have detailed knowledge of what's being done now.

How would such a "smart monitor" connect to the Internet? Wouldn't that require network hardware not commonly found in monitors as well as some cooperation from the owner (to hook up the monitor to their network, with unclear benefits)?

I'm really not sure how that works, since you're asking me. The mechanics of allowing your monitor to connect to the internet is irrelevant to any sane life, as far as I can see. I can see no use case for running Netflix, Spotify, or any similar application on your monitor that would be an improvement over running it on the attached computer, but I'm not really the target audience.

HDMI can pass-through communications. Wireless is also a possibility. "Thank you for plugging me in! Please enter network credentials so I can update myself!"

I just dislike HDMI for a lot of reasons. That is one problem. Another problem is HDCP. Those aren't the only ones. I would prefer to connect audio and video separately. HDMI doesn't have captions. etc.

Due to this, I have my own specifications (not fully written, although I did write a lot of it), which are much simpler than HDMI. (It has digital video (with no inherent picture size limit, although implementations would be limited), analog audio, and an optional IMIDI (which is a two way command stream; it is safe to avoid connecting it). The IMIDI can be used for captions as well as for control, and can also be used with IR, as well as with the special IMIDI port.) (These would be fully free, although there may be trademark licenses (perhaps to avoid many of the problems that HDMI and others have) but no other restrictions.)

I use a Smart TV as a monitor. I also have a walk/run treadmill where the guards fold down to work as a walking desk treadmill. When I want to get a run in I switch my monitor to the TV side, pull the treadmill out a foot, pull the guard up, and run a 5K.

The one I didn't buy was a Samsung M7