Art in Middle Earth.

[Legate of Amon Lanc]

I think what's been said this far mostly makes sense. Also, just as a note, it occured to me that for the "outside the book" explanation of the little significance of paintings, might be that Tolkien was not so fond of "visual arts" (despite painting/drawing some stuff himself - but he was always also very vocal about how one depiction of a situation sort of limits your imagination to one fixed image of the reality described), so maybe that might also be (by a tiny part, for sure) a reason why he did not mention so much about the paintings etc. (Also, all the paintings mentioned in the book were more "non-realistic" - like, always paintings of random tree or somesuch, never stuff like "a portrait of Eärendil" etc.)

But the "statues and co. are much more appropriate, medieval-like style" seems to me one of the best and most logical arguments this far.

The important "paintings" (or drawings, rather) mentioned are, for example, on the maps (dragon on Thror's map), so it's a part of a "different genre", so to say. I quite like that, though. Not sure if I can explain why.