A possible impediment to company support for this would be the rise in sponsored / promoted posts used by apps such as Twitter and Facebook. Users might want to be muting things that appear in these advertisements and if a company makes these un-mutable then you have user satisfaction going down.

Of course this a concession users might have to make in order to reap the benefits of such a system. It is a good idea, though dubious it is the 'future' of the internet especially since it exists in a self-contained platform that is opt-in by its nature.