I wash my hands quite frequently and both my iPhone and iPad screens still collect fingerprints like crazy, so while it's helpful and good to keep your hands clean, it's hardly a solution to this problem. The fingerprints annoy me, but this is how it goes with most touch screens and I'm used to it at this point.
Hopefully some kind of screen technology comes along that is highly resistant to fingerprint oils. In the meantime, I always keep a good microfiber cloth close by and wipe my screens often.