Why so obsessed with bass?

Sub-woofers are an interesting phenomena in that they are relatively rare in 2 channel systems in Europe, where they are found mainly in AV theatre systems. They are, rightly or wrongly, often perceived as unnecessary to a pure 2 ch system. The theory being that if a speaker is done right then you shouldn’t need one.

The US market seems more fixated on them, and in the plural as they seem to come in multiple subs in some US systems.

We have smaller rooms in Europe, maybe that’s why too, no room for more wooden cabinets. And we rarely have room for a dedicated Hi-Fi room, usually it’s a home lounge too. If your room only takes a small speaker, that is the type of speaker which most benefits from a sub, then you’re unlikely to be able fit more boxes in. If your room fits a bigger speaker you shouldn’t need a sub.

When I have heard systems with arrays of multiple subs they have sounded to my ears too much. Or when toned down I have heard them sounding good, but not 4 boxes worth of goodness.

Everyone has their own opinion as to what is good bass. A teenager who has 400 pounds of amps and speakers stuffed into a Honda Civic may like to see birds flushed from trees frightened by the booming coming from the car. If that's their goal...good for them.
Personally, I prefer bass that is what I perceive the creator of the music intended. Often that's hard to know. Bass preference is an individual subject. How to achieve YOUR preference?????????????

Had to laugh when I read, "its actually about QUALITY, not QUANTITY" because, with subs, you need quantity (more subs) to get quality (better bass).

Have noticed that newer speaker cabs are including smaller drivers. Mostly cause people want smaller spkr footprints.  Of course this impacts fullness and quality of bass from main speakers.  
To solve problem, dealers advocate subs.  Marketing genius.
More boxes higher sales.  
My older speakers have larger drivers and fill room so much better.  Imaging not as good but very nice to listen to.  
Size of drivers matter for bass.

Answering the first part of the question, "Why subs?" - because music can include frequencies in the human audible range, 20Hz to 20,000Hz. Most speakers (towers and otherwise) can't play as low as 20Hz; therefore, as a listener, your potentially missing part of the music. We can't hear what the speakers can't play. Would you fully enjoy a painting if it was missing some colors? No, it would be incomplete and likely unbalanced. Avoid the necessity of subs by choosing "full-range" speakers. Why companies make floor-standing speakers that can't play down to 20Hz is a mystery to me - who could possibly want this (unless they intend to add subs in the original plan). To me, these companies are like artists intentionally painting incomplete pictures... a 'novelty item' - no thanks.

The second major issue is how low frequencies (long wave lengths) are affected by physical room dimensions. Very few of us are listening outside in the middle of clear open space. Instead, we are typically listening from inside a box, and those walls, ceiling and floor create peaks and troughs of interesecting air pressure from reflections. These bass nodes change the sound (distortion). How to solve it? Room treatments and multiple sources (multiple subs spread throughout the room) - the more subs the better. Not for more bass volume... for more linearity throughout the room. Additionally, higher quantity of sub drivers (more subs) allows each individual driver cone to move less while summed together achieving the same volume. Less excursion means more accurate cone movement ("fast bass"). Again, more subs is better, but beware - like anything else, there is a curve of diminishing returns regarding value.