How important is bass to you?

Inna,
I think most responders will agree with your preference. Bass is important as are all the frequency ranges. We want them "all" to be good. Given the context of the question,I place more importance on midrange than I do the bass region. If your question is meant as a hypothetical pick or choose compromise, I'd choose good bass with great midrange rather than great bass with good midrange. I may be in the minority.

By "except the lowest bass" do you mean the bottom octave (20-40Hz)?

Hugely important. Like Prcinka I went through a stage of buzzing on the midrange, then swapped in some rft ecc82s and reached nirvana. You have no PRAT without a prominent rhythm section. Nor do you have the fundamental notes that make music sound so beguiling.

Many instruments can get quite low, not only pipe organ and acoustic and electric bass. And voice can get low too. There is a huge difference between a system giving you some bass at, say, 30hz and the one that plays it just as well as 50hz.
I was listening today Hellborg/Velez Ars Moriende album. The Love Death Ritual track is excellent. His custom acoustic bass guitar goes very low at certain moments. But my system gives me 'some bass' at 30hz, there is a lot more in the recording. I was upset.

Clean clear bass is more important than BASS; often the crossover is just as important so that you can hear a distinct difference between the low-midrange instruments vs strong bass lines in an ensemble. To get the best LOW bass performance, the room acoustics become extremely critical, as does the upper treble frequencies (too bright AND too boomy). For me the final answer is, as i am
using my living room as a listening room, to find the right volume level. I have way more stereo system than my room can handle (i often wish i had stuck with a smaller pair of speakers but a good deal came along, etc.).
IN conclusion, the more you hear "clearly", the more enjoyable the experience of listening over extended periods of time. But if, in the end, you aren't going to be satisfied with less than 20Hz bass, you're going to have to address the other issues i mentioned above.