There's a lot of reasons. If I had to narrow it down...

For starters, Itachi didn't want people to know. I'm going to respect that. [He's given up a lot already - it was the least he could do.] He's a grown man, and if that's how he wants people to see him, that's his business.

But more than that - and I've given it some thought - it just doesn't make sense to. Knowing will just make things troublesome, and could cause you a lot of grief while you're here. The less you, or anyone knows, the better off you'll be.