After all, speakers do need EQ and which is done either in the passive or active crossover.
With this in mind, you ask a valid and important question. EQ of the room response will almost always comes with some kind of compromises. Raising low frequency dips wil for instance increase distortion. Reducing low frequency peaks with many dBs will often reduce dynamics and make the response worse in other parts of the room. And neither of these deal with the harmonics of the frequency one is addressing. Most of the room response isn't minimum phase behaviour, meaning the phase will not follow when the frequency is changed. This will lead to phase distortion. How audible that is very much depends, but generally is much more audible for midrange and treble than lows.
However, using shelving to tailor the response to the room/placement and music taste without doing anything with dips and peaks is fine. And it's also needed considering we listen at various distances and have different reinforcement from the boundaries.
Room treatment doesn't suffer from the compromises EQ has and actually makes the room response more minimum phase as long as the treatment is of high quality. As long as we are listening with boundaries, the room will effect the sound quality greatly no matter how good the speakers are. Naked paralell surfaces will create flutter-echo and comb filtering. The close proximity of boundaries create standing waves. Especially the important time domain behaviour and certain psycoacoustic cues can only be improved with physical treatment.
That being said, speaker design react differently in rooms. You can take two different speaker designs, and one will measure considerably more even than the other. And while treatment can get them closer, some room interaction isn't easily treatable. For example the floor bounce. Thus a great speaker design will take the room into consideration and that's always where we want to start. Creating problems that needs to be fixed later is never optimal.
So with that in mind, there are speaker designs that are to some degree "flawed" or of less quality. Many of the speakers that we see scoring high in spinoramas are in my opinion quite mediocre. Place them in a room, and the response in part of the frequency range will not be particular even and there are other issues like intermodulation distortion and thermal distortion. Fixing uneven response with "room correction" doesn't work very well, and the distortion issues can't be solved either. Correcting parts of the uneven response with treatment is difficult and sometimes impossible.
So start with the very best speaker design and desired beamwidth, treat the room as well as possible, and use EQ to tailor the general response by listening. Most likely you are not going to need the multiple subwoofer approach or EQ in the lows to achieve a flat bass response with the combination of optimizing placement and room treatment in such a room.
