What is the privacy leak vector using lynx? It does not use JS, so I'm not sure how running wget on another server is better than lynx over ssh or mosh?

I don't know, we're both speculating. I'm just advising against "oh he could just as well do X" - you don't know.

I assume it is more about structure and time. If you start browsing you wait for pages to load and then probably go a page further and to the next. In the batch mode you have the designated time window to go through mail and read what is there and avoid jumping into some rats nest of neverending paths.

In addition you get those privacy aspects (website operators don't know where you are) and are blocked from "non-free JavaScript programs" and only deal with text with content, all else will not come through.