Alembic players know about this. When I got my first one, I could hear my notes between what sounded like hard rain on a tin roof.
Kept the same bass. Same strings. Same amp. Double checked my setup (sorta low/straight at .010" relief) and my pickup heights (though you don't get the treble bloom as they get closer to the strings as you would on high-impedance/passive pickups). Worked on both hands, mostly my left/fingerboard hand.
After a few months, I was 'clack-less'.
Whether it does it or not on your other basses is not the problem here. I'm betting, that like when I got my first Alembic, it's technique, and the bass in question is good enough to let you hear it. It's not stainless steel frets instead of _____________. Just like low action requires some modification in your hands to play cleanly, it's nearly the same thing stringing up with really bright strings and lots of top end. When you can hear everything, it's far more revealing than playing a PBass with flats.
I'd also posit that the same way the deep bass we hear is NOT the fundamentals typically, you can run a very bright tone, but restrain the very highest part of the note in your tone setup: You still get a lot of articulation and brightness, but you can round off the very top end and save yourself some finger noise, both in tone on the bass, and on the amp if your EQ options are broad enough. Think of a passive bass like a Precision or Jazz: Run the tone wide open, you'll hear any rattle that's in there. Back it off just enough to subdue that and you've still got a lot of top end that's now far easier on the ears!
To me, this one of those questions that has no big single, light-switch answer; it's gonna take a little modding here, and here, and here.