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If an amp has a sound, it is unlikely that it is audible in the very low frequencies that the sub plays. And since the sub has a class-d amp, if it has a signature, that would override any signature in the main amp. In other words, his listening tests are unreliable if that is what he is observing.
I tried both connexion modes and prefer line level. In high level mode I had no options for bass management except from the sub in addition to no room EQ from the then stereo amp. Paul mentioned he shares that opinion with a colleague at REL.
In case it wasn't clear: I wasn't trying to make a case specifically for how the REL subs are deployed. I was only responding to what I took to be your general question of why anyone would want an amp with a sound quality signature.
(Btw, one of my very old old tube amps, the Eico HF-81 14W integrated, certainly seems to have a substantial sonic signature in the bass. Seems to bloat the bass in a way that leaves an impression of "bigger, deeper" bass. When I use it on smaller stand mounted speakers, it makes them sound even bigger. The amp measured pretty wacky in the stereophile tests, but I friggin' love the way this amp makes my speakers sound. Maybe not an audio destination, but a really fun place to visit!).