You have to keep mobile and desktop OSes separate. Mobile OSes are for use on-the-go and mainly focus on content consumption and getting most out of a pocketable touchscreen. Desktop OSes, in contrast, are for productivity. People understand browser tabs, how would a tabbed chat window be so fundamentally different?
> Modern email clients also follow this design paradigm.
Email clients are different. You don't usually jump between messages/threads back and forth like you do all the time in IM clients when you're actively chatting in several conversations at once. You open them one by one, read them, and go do something else after no unread emails are left.