Activity Stream is a Formatter, and formatters can only be added to Forms.
It is not possible to add any formatter in Lists, activity stream is no exception and therefore, unfortunately, Activity Stream cannot be added to Related Lists.
Also, activity stream does not come from one single table, it has multiple sources and often the sources are dynamically generated. Therefore, it is not possible to add a table as related list to replace the functionality of the Activity Stream.
Release or Environment
Madrid, New York