What you are lamenting the lack of is the 'presence' indicator, where you can set yourself Available, Away, Busy, or simply Offline. Of the current crop of IM clients, only Skype still has it (I think).

Of the older IM clients; Lync had it, so did Lotus Sametime, MSN Messenger, Yahoo Messenger, ICQ, and of course AIM.

Somewhere along the line the presence feature got dropped, and now we're always 'Available' even when we're not.