Audiophiles' desire is that bass should have articulation, energy, speed delivery, and coherence. This desire is erroneously given the name of "tight bass", although for legitimate reason: the main barrier to good bass was looseness, lack of definition and energy in the past.
Now, when we correct the lack of energy, definition, speed and dynamics, then we get good bass. This is also experienced as the bass "tightening" as audiophiles say. However, the "tightning" is an improvement only to a certain degree, after a point it becomes just as much a coloration to sound as the lack of focus is.
Good bass has articulation, energy, speed and coherence. Yet, it is neither overly tight, nor overly loose. A common problem with audio systems is / was their inability to reproduce clean and coherent bass, and people (audiophiles) summed this up as "loose" or "colored" bass. However, most audiophiles do not realize that coloring applies to BOTH ends of the palette: bass can be colored either to be too loose, or to be too tight. Over thight bass is just as colored as overly loose bass.
My observations tell me that the fascination with overly "tight" bass arose from people using studio recordings as reference, where the hall acoustics information is lost, resulting in an overly dry, sharp bass rendering. To me that kind of bass is unacceptable, as it is missing a lot of the textural information, the three dimensionality, and reaches a point where it blends the clipping/distortion characteristics of the system. (Which occur much, much before audiophiles realize it.)
With over-tight bass you are also missing out much of the technique of the player. In the case of drums, the systems described as having "very tight" bass render the drums as if the drummer was very very strong, punches the set with double impact, but his technique is missing out a LOT. Basically, we get a mediocre drummer with very strong arms, dominating the band and the midbass. The other end of the spectrum (described as loose bass) describes a situation where the drummer is weak, there's no energy in his snaps and kicks, the tone is smeared, and we can't focus on the technique either - I get no information whether the drummer has good or bad technique.
The truth lies in between: bass with proper energy delivery, proper timing, textural definition, proper dynamic range.
Focusing on "tightness" to me is turning your system into a sharpness filter, coloring the sound, removing you from high fidelity.