Father's a postal worker. Easy answer- HELL NO! UPS runs their workers ragged for little money.
My old man is a letter carrier. Typical disgruntled postal worker;)
I don't think it should be privatized. Rates for a letter might temporarily go down with competition but they would eventually rise over time compared with the current system. 37 cents for a letter is pretty damn good. There is not much profit potential for letters anyway and there already is ample competition on packages. You also can chose to send your letters with any company you want as long as you are willing to pay for it.