I use invisibility all the time. I am also always offline on FB. I don't know why, but I don't like being tracked either or appear available. The problem is, there is no way to know how others view your profile, as in FB, for example. So, you can see your own last log in and what you are reading now, but I am not sure if others can see those information under invisibility option.

Also, I guess people can always PM or visitor-message others if they are concerned about them.