The keeper of the royal stool apparently wipes the ar#e of the King.
The a/c are only allowed into LHR to permit a more useful/profitable role for an airbus. If the mainline company is ever successful in it's core business the EMB's will go back north or be sold if there are no suitable niche routes which fit the Regional business model.
To your original point Regional uses the AIMS system to roster but does not run particular paterns as you describe. Sometimes you get 1 on 1 off other times 6 on 3 off, generally single days off are to be avoided. You can expect weekends are most likely going to be in a hotel on the Bath Road all next summer as mainline have taken on an extensive charter program to pay the bills accumulated operating in LHR fog last week whilst everybody thought the airport had closed and the CEO didn't see fit to advise the media otherwise.