I've seen this too. It's quite painful:
I have a dense menu with a lot of controls - each with a tooltip, and if you move the mouse over
the menu, tooltips go up and down quite frequently, causing a lot of these hidden divs to be created.
I work in accessibility, so I'm not against it :-) But this behavior really isn't helpful in the
sense that one mouse movement is giving a log that has the same data repeated 10s of times.
Suggestion: Set a timer and only make a log entry when a tooltip stays up for some reasonable
minimum time - say a second or two. That would keep the log, but reduce the noise. (Note that
virtual mice can move more slowly than real ones.)
Suggestion: Number the log entries. If making an entry that is within a reasonable window of
another copy of the same text, enter something like "Dup of #10" instead.
In both cases, note that bandwidth to the user is also a precious resource - voice and Braille are both
slower than optical reading. So avoiding thrash and collapsing duplicates is a good thing.