"can you or can't you create a filter with an inverse response to that?" I think that you can.
But, I'm not sure how I feel about the idea that a room will have a linear response with regards to any practical or real life experience. Isn't that why "anechoic" chambers were invented?
One would think that a rectangular room with bare walls can have predictable peaks and nulls right where the math says they will be, but every time I've run a RTA test in one I have found that the results vary from the anticipation.
Discounting absorption of wall surfaces and presuming constant surface reflectivity characteristics, I'd want to learn more about:
Is the impedance of air "linear"?
Is RT60 Frequency dependent?
How does varying *musical content* energize a room compared to an all pass sweep or chirp?
It seems to me that the synthesis, as a room is charged with energy featuring differing frequency components, will create varying interactions with results that differ from an idealized flat response.
That's why I keeping thinking, wrongly or rightly, that a system needs to have an active component to make corrections that achieve the results that are suggested by displaying a flat line.
If ARC et al. actually provided an opportunity to test its results instead of simply drawing a "predictive display line" I think it would be very informative.
Corrections welcomed!!!