This question is much more complex than it is being given credit for.
Two examples, from the extreme opposite ends of the spectrum. At the extreme low end, really good bottom end reproduction improves the sense of envelopment and improves the sound well up into the midrange. This is the case even when there is no discernible low bass present. I heard this when first going from one sub to 4, and again when putting all my subs on Townshend Pods. In particular with the Pods I distinctly remember being surprised because I was expecting and listening for low bass but what hit me instead was the greatly improved imaging and envelopment. What was surprising was the low bass I had put the record on for hadn't even started yet.
Something similar also happens at the extreme high end. There the addition of Townshend Super Tweeters would seem to only affect from about 15kHz and higher. But yet in this case clear improvement is heard well down into the midrange, and even some pretty low bass sure seems to sound more tight and articulate with greater clarity.
For these reasons I think it is overly simplifying to talk about frequency bands as if they can be viewed in isolation. They can, of course. But only by discounting a lot of really significant phenomena such as these.