Why do so many people have problems with bass?

OP, have you heard a system and room with really good bass? If not, you might not know what you're missing. 

People who realize they have bass problems usually will comment that it’s not the sound of the bass itself that is problematic, but sometimes you may hear them say that they are not getting the attack, texture and definition they would like.

As many have commented, these bass problems deal with how the speaker is interacting with the room. Most systems will have some bass reflections that cause both room mode issues (excessive gain in a small window of frequencies) and phasing issues (where the waveform conflicts with other waveforms at intersection points and manipulate or cancel them out). For example, an 80 Hz wave cycles four times and can intersect with a 20 Hz wave in a particular instance, which could amplify gain or nullify it based on its phase. In these cases, what is happening then is that the bass is “muddying up” the remainder of the frequency spectrum.

As hilde45 says, many are not aware they even have issues and are not aware of what they are missing. But when these issues are resolved, the tonal balance improves, and each frequency across the spectrum is better defined and perceived, helping the system itself to sound more immediate and resolving.

The room is key, but so is proper amp/speaker integration. I had great issues with what's known as one note bass, an overly resonant, booming bass in a couple systems some years ago. I tried to fix room with great use of tube traps, double stacked in four corners, moving speakers and listening position to avoid standing waves, nothing I could do to solve issue. I then concluded amp/speaker combo I used in both those systems was the culprit. I loved sound of tubes on mid and tweeters on both speakers, damping factor of those amps not enough to control woofer. I would have needed to biamp those speakers, tubes on top, solid state on woofers to get the coherent sound I was looking for.

Good bass is tuneful, articulate, opposite of one note, boomy bass. The other thing you'll find extremely noticeable once you get rid of boom is far more resolution in mids and highs than previously experienced, boomy bass covers up much of freq. spectrum.

And to answer your last question, while bass interferes with the full frequency spectrum, most room mode problems manifest in the 45-95 Hz range. 

Room size doesn't affect bass range even a car can support under 20hz as do headphones. Most bass issues are caused by overly small loudspeakers that have overly small baffles and little below 50hz many have a titled up response around 80-125hz so they sound like they have a lower bass response thank the BBC for that. If you end up with a space that re-enforces a lower frequency node multiple bass sources can greatly reduce it. As I type I sit in front of a giant with 4x21" woofers I use these near field most of the day in my office. I have no bass problems just great bass and pressurization of space.