There's definitely a way rooms could be phased, but the issue is that Revit's likely too rigidly coded in the backend (at least for rooms). Since Autodesk didn't originally create Revit and they historically have shown no interest in rebuilding it from the ground up to address some glaring design flaws within the software, we will likely not get phased rooms despite the technical feasibility and practicality that system would offer. And with Revit the way it current is, as much as I want phased rooms, I would have to say no thank you because to make it work would likely require too much calculation on Revit's part and just further slow down the already outdated software. Just another issue grandfathered in thanks to Autodesk's unwillingness to give proper funding to dev teams and guidance for prioritizing new vs revamped features.
As for the how, I think there's a little bit of a limit on creative thinking happening from metisdesigns, as it would not require a rework on the room boundaries to make them extend beyond their constructed and demolished phases, but rather the room elements themselves and how they're calculated. Simply have each room calculate which boundaries contain it for each phase the room is in (excluding it's demolished phase). If the room is in 3 phases (Existing, Demo Phase 1, Demo Phase 2, with the last as it's demolished phase), it has 2 calculations to the boundaries that are in those phases. Resource demanding though it may be, these boundaries would then be stored into a database that each view accesses to determine how to display the room based on the phase of the view. This data would also have pointers to the room bounding elements it extends to and listeners on both those elements and the room in the case of a bounding element being placed within the room, and only update the rooms as needed rather than recalculating the model on every single element change. The biggest issue that would cause the model the most fuss would be if a single ceiling/roof/floor element with volumetric calculations turned on, as it would interact with and alter multiple rooms simultaneously. You would also, possibly, still have the issue of how to display previous/next phase rooms, and would likely just need to disable phase filtering for rooms as a result, but I think that could be worked out if the rooms are simple not displayed at all in their demolished phase. But the reason this is likely not feasible in Revit at the moment is that rooms seem to be a hybrid element; they act like they are view dependent, like annotations, but also volumetric and interact with model elements. But even this thought isn't the whole truth and we see how phases could be implemented with the ability to turn on room volume calculations that then limit the vertical extents of the room to floors and roofs/ceilings.
Another misconception I think is happening is that, as rooms are very data-dependent, they cannot persist when there are major changes to the room. Unlike with walls, where model elements can be added or removed in different phases, element parameters are immutable. Just like if a you were to change a wall type from GB+||+GB to GB+||, you wouldn't change the wall type in a phase, you would demo the original wall and place a new wall with the demolished phase of one and created phase of the other set to the same phase, essentially "hacking" the demo graphics to show the demolished gyp layer. To change room data (number, name, wall finish, project parameters, etc.) is to fundamentally change the room; these rooms would have to be demo'd with new rooms placed with the new data. My above suggestion for how rooms could be phased have no bearing on this matter because they are mutually exclusive subjects, and this is how Revit and element parameters will work regardless of whether rooms are phased or not.