If you were to cover up info such as address, DOB, or whatever, while it won't make a difference to the TSO since we don't look at the address anyway, you could potentially open up a discussion about presenting an ID that has the appearance of being tampered with. I'm not saying it would happen, but that's a possibility I could forsee.
But as long as I can see what I need to see on it, speaking for myself here, wouldn't matter to me if your address was covered.