except that a room doesn't exist without the bounding elements, each of which can have their own phase.  
 
what you're asking for would require that each room bounding element would have a room boundary that goes both forward and backward outside of it's construction and demolition phases, and that each room would have a node/origin that would extend to any bounding element.  if i demo a wall between conference room a and b revit would put multiple rooms in the same volume.  
 
this would further become a huge nightmare when you actually try to place a room in a remodel where you've demo'd old walls which would divide the new room.  you'd have to demo room bounding wall's room boundary at a different phase than the partition itself.
 
copy and paste is *not* the end of the world.  you can select all elements in project or view.   even if you DO have more than a handful of phases you need to chase rooms through your project on any of the solutions proposed would make things much worse rather than better.
 
the only way i can see rooms pushing across phases is for the room to detect the start and end phase of each of it's bounding elements, and include itself in phases where ALL of the elements in the room are the same.  even then, that will cause undesired behavior when a room gets a new use in a new phase, and has to be demo'd discretely from its bounding elements.   further if it DID persist, and you wanted to paint the room in say phase 2 room finish schedule, revit would have no way of understanding that it occurred in phase 2.   (now revit material paint having a phase, i can get behind)
 
 
case in point, i'm doing a simple tenant build out study of a warehouse/office space at the moment.  of the (10) rooms in the existing building, none of them will retain the same name in the buildout, making them entirely different "rooms" in revit in the new phase.  (8) of them will not change their volume or walls, but will have different uses, some will get paint or carpet cleaning, and they'll be different "rooms" even the existing water closets which are going from gendered to unisex.
 
 
seriously folks, "rooms" in Revit are not the physicality of conference room b or the north end of the cafeteria.  they're a way to discuss the extents of a particular volume at a particular point in time.  if you want to talk about office 102 last week, and the same office when the hallway to it has changed, you have to remember that intellectually we know that time has shifted, but from a revit database standpoint, that has to be spelled out.
 
 
in some cases it would be handy to have rooms propagated. i can see it being useful to have them able to  link across phases to "themselves" IF they had absolutely no changes, but something almost always changes.  
 
 
zombie horse beaten back down again.  
if you're pondering thread necromancy, please, go back, and read, then re-read my prior posts on this thread.  i feel like a broken record.