The main reason is for safety. Our safety, and the safety of people we care about. Heroes make a lot of enemies among the people that they stop, people that would almost always rather strike at us when we're vulnerable, or take someone we care about hostage.

I personally prefer a more open, honest approach, but I know someone who had their family killed because of a compromised identity. That's why it usually has to be a secret. However, I've been 'out' for a few decades now.