"Tolkien himself said that he wrote LOtR without social commentary. And who said it had meaning? Sometimes a book is just a good read."
Yes, but I doubt he said that it lacked a broader social meaning (by which I mean that it had ideas that pertained to society...I mean, the book clearly has ideas about good and evil and the nature of both, and that's always something that pertains to society, yes?)
As to the second part of that--I disagree...
Not everything is or has to be Hamlet-deep, but even something that's just "fun," like LOTR or Sherlock Holmes, can have meaning.
Again, it doesn't have to be a deep meaning, but it does have some, even if that meaning is just "good is good" or "being logical and analytical is totally awesome...and sometimes not so much."
"I think sometimes we over-analyze authors and artists."
Fair enough, but I also think there's a tendency and danger in going the other way and not giving authors or artists enough credit, or being anti-analytical.
There's a happy medium between "Hamlet's just a dumb emo mopey goth who can't decide to shit or get off the pot" and "Hamlet is a Marxist Deconstructionist commentary on power relations with respect to the hegemony and proletariat as it pertains to the thing in itself so far as it is itself or ever can be."
The former's overly-reductionist and stupid, the latter's intellectual masturbation...and stupid. :p So, a happy medium.