Perhaps Frodo is also depicted as a celibatary "old bachelor" in order to save him such a conflict of duties?
I don't think you really know if he was celibate, you are just assuming it from lack of data.
Tolkien omitted writing anything about the sexual mores of the hobbit, because it just wasn't considered polite, in his day and age, to spy on the bedrooms of others. Frodo, as well as Bilbo, may have kept a mistress in Bywater or its environs. However, your point about no children is a given, and your reasoning why is sound. :)