Historical use of figures in geometry I was surprised to learn from John Stillwell's comment in answer to the
question,
"Can the unsolvability of quintics be seen in the geometry of the icosahedron?",
that

There is not a single picture in the whole ... 

of Felix Klein's 1884 book,
Lectures on the Icosahedron and the Solution of Equations of the Fifth Degree.
And now that I have it in my hands, I can verify the lack of figures (but its
remarkable clarity nonetheless).
By the time of David Hilbert's and Stephan Cohn-Vossen's 1932
Geometry and the Imagination (citing an earlier MO question), 
the use of figures had reached a high art.
This high art is continued today in
Tristan Needham's Visual Complex Analysis, with its stunning figures, e.g.,
(from this MSE answer): 
      
To return to ancient times, it is clear that figures were
valued to illustrate Euclid by 100 AD, and likely earlier:

Finally, my question:

Has the use of figures to illustrate geometry waxed and waned over history
  in a fashion that could almost be graphed with respect to time, or am I plucking out
  idiosyncratic examples that do not point to any recognizable trends?

Perhaps this needs to be mapped country by country, different in France
(during the Bourbaki period) than in Germany, etc.? Or perhaps any such attempt to
capture gross trends is hopelessly historically naive?
 A: You may enjoy Reviel Netz' book:  The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History. Cambridge: Cambridge University Press, 1999. 
It examines the use of letters diagrams in Greek deductive practices. Of course, my suggestion does not answer your question directly, but I am hoping that it sheds some light on the whys and hows of using figures over times. 
A: The Sangaku  problems of Japan's Edo period are worth mentioning here. Also see Sangaku: Reflections on the Phenomenon for some cultural history about it.
A: There isn't a single diagram in Weil's Foundations of Algebraic Geometry (1962, 363 pages) either.
A: Some other books of Klein (Fricke-Klein on authomorphic functions, his Lectures on hypergeometric functions) have a lot of excellent
pictures. From reading many old mathematical books I cannot conclude that there was any trend
or fashion that changed with time or from country to country. 
The explanation why some books have pictures and others do not is probably simpler:
it always was (and still is!) very difficult to make good pictures.
At the time of Klein, a skilled engraver had to be hired. Reproduction of the pictures
probably substantially increased the cost of printing.
In our time, many mathematicians (including myself) do not know appropriate tools,
and don't want to spend time required to produce good quality pictures.
Reproduction of old pictures in new editions of the same books is probably also
enormously difficult and expensive.  
A: Maybe this isn't an answer, but below is a photograph of the tablet BM15285 (British Museum catalog #15285).  It's a series of geometry problems, from c.1800 BCE (+/- 200 years?).  There are plenty more Babylonian and Egyptian mathematical texts with illustrations.
I don't think the waxing and waning of figures in geometry is such an interesting question by itself, and I don't know what we'd learn from such a graph.  What's in the figures tells us something about the geometry at the time/in the culture from where they came.  The figures also reflect the writing and publishing industry at the time -- whether carving tablets, hand-drawing on papyrus, mass-printing and typesetting, etc..  

