The stories in this thread pretty much confirm my experience's with these types of "enhancers" (and many of my friends).
I feel like BBE or Aphex "processors" are one of the first "effects" that beginning bassists try out. The eq curves tend to attenuate midrange content giving a perceived "bigger" or "clearer" sound. This can definitely make an inexpensive rig sound gutsier, but it's really an equation for trade-off. Less detail in one frequency range exchanged for more in another...
It seems that as a bassist learns more about technique and eq (and obtains higher-quality gear), that the "maximizers" and "enhancers" end up abandoned. For example, you have a "light-bulb" experience one evening where the unit is forgotten or not used for some reason & the user finds that they prefer leaving the effect home! Gaining experience with how to use eq (and
not use eq) properly also goes a long way to marginalizing an enhancer.
I've worked in a lot of world-class studios and played a lot of the best stages in the 'States & abroad. The only time I've seen BBE or Aphex maximizers in use was at project studios or churches, and at the occasional dirty rock-club. The price points of these units is set low for a reason, I believe.
(Now, before the attacks) if you use a "Sonic Maximizer", or whatever and it works for you - well then great!

Seriously, there are no set rules and diversity in tones & approaches makes the bass tone world interesting! I suspect you'll eventually abandon it, but if not- that's ok with me. I'm just sharing my personal experiences and observations.