Very good point indeed! However, Tolkien himself stated that he did not dispose of a tremendous sympathy towards Celtic mythology (to say the least). I found that quite paradoxical as there are many references I can see in his works concerning Gaelic culture and even some Celtic languages (most notably the correlations between Elvish and Welsh/Irish/Scottish Gaelic).

While Elvish was truly based on multiple languages, there's a clear Celtic influence I can see (at least, this I believe is obvious while we're speaking of the films directed by Peter Jackson). Here are his thoughts on Celtic mythology: http://en.wikipedia.org/wiki/J._R._R._Tolkien's_influences#Celtic_mythology