I suppose that Art must also be considered: "Four rings for the Elven kings" just doesn't sound quite as nice as "Three rings for the Elven kings." Then again, that's just Sauron, writing his binding-verse, and he never appears to have even considered that one of the Three was never owned by an Elven king, lord, or even male (other than its maker, Celebrimbor).
I have also suspected, rather more seriously, that Tolkien went for three rather than four as a symbolic nod to the Trinity; he does admit, after all, that he rather intentionally thought of lembas as something akin to the viaticum of communion, which was why is became so strengthening and sustaining the more it was a person's sole nourishment. This would seem to fall into that same kind of symbolic (not allegorical) thought. Then again, he may have started off with a thing for prime numbers, until he got to the Nine.
