No current plans to include a feature to remove the activity stream but we are considering to make the stream more flexible in the future. Just not planned at this point.
If you are not already doing this, I can recommend spending some time to hide the updates not relevant for you personally - this makes the stream more relevant and creates a faster way to get overview of the activity in your company.
We see notifications on things you actively follow as what you need to know, while the stream is a way to discover things in your business you might not know (nice to know) and enable you to follow and participate in discussion, even if you are not directly involved.
Thanks for the feedback, please keep voting.
/Sara - Podio