Though there is plus-sides, there is minus sides of it, too. IMO the present chat rooms are enough, and there is no extra need to show off anyone's presence.
1. It causes distraction:
It would be rather irritating to get to know when the other users are online and showing other users when I'm online. It will kill the focus to write a question or answer, and also may encourage spam and junk.
It is very okay and nice that when users get time, they come, reads the q/a and comments, and leaves their response accordingly.
Also I love very much a side of SE network, i.e. it is not obsessed to persons, but to subjects. I do not have to compulsorily share any personal details or academic credentials, (just like I do not need to tell when I'm present or not). Similarly I can't follow a person but can follow a tag. But in urgency, can leave a comment to anyone, no matter of 'friends list'.
- 2. It may cause a trend to ask a question only certain user is present; thus may reduce the reach of the question, and will also the diversity of the answer
I do not think there is any need to address a question to an individual from the moment of asking. if a question get quickly received by 1 or a limited number of users, quickly accepted; and then get dumped as answered. And just solving someone's question is not the purpose of this site. The purpose is how-much the world can receive and use the knowledge you shared, for future.
If a question stays unanswered for a longer period, say a day or few days or an week; peoples from versatile backgrounds will get to visit it while browsing, and will try to solve it in their own ways of thinking. Also the question will get more reach, attention and care. Simultaneously, peoples from specific field, too, would come to the question while they will search questions by the tags they are interested in. Even it could happen; whom you were thinking to knock, will show a distraction to the question whereas a person from some other field would give you a satisfactory answer.
What I prefer, is to submit a question, and temporarily forget it (and doing own works). Later-on I check, in which way it grown. Or what surprises waiting for me.