I think this is just a simple step toward a complete rework of how phases interact with objects. Phases should also be able to interact with other parameters within a family. For instance, using it to drive the swing angle of a door in plan view.
I do agree though it would be great to be able to tag phase information. Currently you can only schedule phase info.
As for making it usable in formulas, that would be great but they would need to be implemented in a way that the formula in the family would pull the phase name from the project so that families work in any situation.
If you made a family that did something if a door is created in either the new or existing phase but then your project has a 3rd phase and the door is created in that phase what would happen?