It would sure be helpful to be able to message living descendants of a common ancestor with oneself to see if they have information of help and to sign up to receive for messages from them, too.
You could do so through the current collaboration options within FamilySearch (enabling Relationship Viewing, and Directory Search, Collaboration tab and creating Family Groups). However, to do so efficiently would require all the descendants to have a FamilySearch account and enable these options and actively collaborate to get the group established. As it is - only those active may come in contact - which makes it more difficult to establish such a group - or when Rootstech rolls around use the relationship viewing options to view descendant/cousin relations and establish Contacts.
Relatives at Rootstech feature was basically a proof of concept of your Idea - FamilySearch could do it - but there may be privacy reasons for why they can only enable it during limited timeframes such as Rootstech (enabling the relationship viewing during the conference was in a different/contained app that closed about a month or so after the conference).
RelativeFinder app through BYU FHL does allow establishing Community groups - perhaps this would be a good place to just start a Family Association/Group to gather Descendants of ______ and _______(common ancestors). If you build the group - maybe they will join - and then from that group establish the Family Group in FamilySearch.