Are you a major persona that can demand, and get, network coverage? If so, forget about them. People still read, and local newspapers, especially weekly freebies, are always looking for content of local interest, which includes the thoughts of local citizens.
An important factor is the writing. You must be straightforward and factual. If something can't be substantiated, it didn't happen. The meme at the top is a good example. It noted the who, the what, and the source. If your letter concerns this incident, then it is best to cite the date, where in the chain of the email it occurred (original email or a reply ten exchanges down) cite the datebon which it was written, and even the person she was writing.
Things to avoid: don't demand "Where's the outrage". When I get emails like that, I do a little research and usually find the outrage is there, but the person that sent it to me was to lazy to research. If YOU are outraged, take ownership of that outrage. But, at the same time, keep your written voice as calm as possible. Keep it Joe Friday monotone factual.
Every small town weekly paper editor wishes he were the crusading newsman like in the movies. Instead, he reprints press releases from local clubs. He'll be happy to print a newsworthy letter.