Soooooo true! Many years ago, I was told, "Cut first, boost later." For a long time, I didn't understand why. Now perhaps I do ..... maybe ..... I hope.
What follows is a generality. It doesn't hold true in all cases, but it does for most.
Peaks are generally resonances, either in the room or associated with the driver. (Rarely are they constructive interference. The one instance where they
are is between drivers at angles divergent from the best response axis. The cure in that case is simple; find the best response axis.) Resonances are frequency bands of too great a level of energy, so you can "cure" them by reducing the energy.
Nulls in the frequency response, OTOH, are usually areas of destructive interference. These areas occur all throughout the frequency band, but as frequency rises, the nulls become very narrow, and thus difficult for our hearing to distinguish. The bass portion of the spectrum, however, is different. The waves are longer, which means that we can hear (and detect) the null more easily.
But because those waves are longer, they dominate the room's dimensions more easily. Moving the location of the speakers or moving the location of the listener has progressively less and less noticeable effect as frequency becomes lower and lower. (This is why speaker bass response is clearer outside than inside; fewer surfaces for interference.)
Destructive interference is very interesting. Because it is defined as the subtractive interaction between waves, the level doesn't really make all that much difference. So you can have a null that you notice at one watt output, and it will still be there at ten watts output ..... and twenty ..... and a hundred ..... and a thousand.
Notice that I'm
not saying that all nulls are caused by destructive interference. But if they are, you're (almost) screwed.
The reason I say "almost" is that by adding energy to the room in different locations (with resultant
slight differences in phase), you can address the issue productively. The only system of which I'm aware that does this is the one by
@Duke, called "The Swarm". I have heard that there are others, but his was the only one that I knew of.
Jim