I think the true reason is that onñy a small fraction of people are interested in convergence and most people are fine, or even truly desire, to have different devices and experiences.

Millions (billions?) of people are happy to leave their phone in another room when working on their computer and vice-versa. Sure you could use a do not disturb button but it would be a major PITA to have enough granularity to allow or disallow certain app/services to notify you and you would be certain to forget to activate/deactivate it when you really want.