From my experience, there is a better solution than that (albeit an incomplete one).
The biggest benefits of room correction are, for most rooms, achieved at the LF end. The benefits within the midrange (such as correction for reflection and multipath timing issues) are much better handled by simple room treatment. With full range DSP systems (affecting the whole frequency range), in my experience, there is always some loss of quality in the midrange, where our ear/brain combination is particularly sensitive to detecting small ‘unnatural’ changes. Even from theory it is inevitable with ‘full range’ room correction systems that there will be some degradation of the midrange signal, but the degree of this could be quite small; in my experience it is easily noticeable.
So, the better solution:
Instead of using speakers that excite all the primary acoustic resonances of a room, use main speakers with a limited LF extension, then use a sub to give the required bottom end. The analogue feed to the sub can be passed through a DSP unit without causing the degradation of signal quality in the midrange.
With this approach, the signal for the (more critical) upper bass, midrange and HF goes straight to the main speakers, unmolested, without any change; the signal to the sub (to which our ears are much less sensitive) is corrected to reduce the over-excitation of the room resonances. The crossover to the sub can also be accurately controlled to ensure good integration of frequency response AND timing, and the delay through the DSP an be finely adjusted to allow different positions for the sub while making allowance for its group delay.