It's nice when your LTE is published. Most of them, however, are not. (What %age of LTEs are published depends on the paper. I once heard that my local weekly published more than 50% of the letters they received at that time.)
But even when it isn't published, your LTE has many beneficial results.
1) Most honest papers publish a balanced representation of the letters that they receive. If they publish 10% and they don't publish yours, their receipt of yours might tip the balance to publish another saying something like what you said.
2) When you write in response to a story they published, the writer of that story or the editor who handled it is quite likely to read your letter. That's one reason that the letters should be polite towards the story and point out one aspect which wasn't sufficiently developed.
3) The purpose of a news story -- from the point of view of the paper's bottom line -- is to attract readers. Therefore every story which receives reader response is valued. If you write in response to a story on Willard's tax returns, that means that people are interested in stories about Willard's tax returns.