Is it possible to clear the contents of the Activity Stream?
No, it is not possible in the current version.
Will it be part of a future upgrade/enhancement?
This is the first time we got a request like this. We have to weigh it against other improvement requests and apply the 80/20 rule. At this point, it is unlikely we can allocate any development time on this given the priority of other bug fixes, improvements and new features.
No problem. I thought it might be a good enhancement in the future so that the admin of the account can review any and all activities and clear them out at frequent intervals.