Some of this clearly gets in to one's personal philosophy or approach to their system.
For convenience I would describe (broadly) to different camps, describing them:
1. I DON'T want my speakers/system to sound like anything.
2. I DO want my speakers/system to sound like something.
So for #1 I'm thinking of those whose ideal is that (like mentioned in the first post) the speakers "sound like nothing" in the sense of being so accurate as to not impose anything on the signal, like an accurate amp would. They don't want to be aware of how the speaker "sounds" but rather just listen to how whatever the musical signal sounds like through a perfectly accurate system (ideally).
I'm in the camp #2. I want my speakers/system to "sound a certain way," I'm pushing it to "sound how I want it to sound."
One reason I take this route is that I have never heard a system, no matter how neutral that didn't "sound like something" anyway. In other words, no speaker utterly disappears in the chain, with the sound utterly shape shifting in some realistic-level chameleon quality that I could never put a finger on. No. Once I hear some music through any system I feel "ah, got it, now I generally know what music will sound like through this system." No more surprises, really.
So for me since every system will "have a sound" I may as well look for the "type of sound I like best." And over the years I've identified sonic attributes that I find most compelling.
That may seem like I'm just after coloration, but that's not quite the case. I do want certain sonic attributes, but one of them is a sense of music being free of a speaker, and the speaker not OBVIOUSLY imposing some consistent character I don't like on the sound. So generally speaking I've gravitated towards speakers that are at least somewhat (or sometimes quite) neutral without obvious gross colorations to my ear.
Also, while yes I seek to nudge my system to mimic some elements of "the real thing" I don't want a coloration that utterly homogenizes the sound. I really, really like not only the music in recordings; I like the different character of recordings themselves, all the wonderful production choices and techniques that make one recording sound unique from another. I want to be as "surprised" as possible from recording to recording, so again some level of neutrality/accuracy has to be met, and a coloration - even one that I find pleasant for various reasons, can not homogenize too much for me. (So for instance yes I think I hear a bit of coloration that adds a bit more "natural" quality to recordings from my tube amp. But I don't find it homogenizes away the differences in recordings).
So for me I'm sort of juggling two goals that are slightly at tension with one another: 1. I want to hear "the recording" as much as possible. But I don't want things to always sound too much "like a recording" but rather a bit more like real life.
To that end I've experimented with tube amps (and playin' with tubes), and yeah I like vinyl too, but I often listen to my digital source, and a lot of how I tweak the sound of my system comes from playing with speaker positioning in my room, and playing with room acoustics. I have a fair amount of flexibility in that I can pull thick curtains to any spot on any wall, and dial in the amount of upper frequency reflectivity in the room to dampen or liven it up.
I've recently enjoyed a bit more dampened sound for the side reflections (floor has thick carpet, ceiling is actually felt covering acoustic treatments behind), which takes a bit more of the "room hash" away and makes the recorded reverbs and acoustics that much more distinct. So, I love the changes I'm hearing between recordings.
But...that loses a bit of the "it's live happening in front of me" sound.
To that end I've found that placing a curved diffusor beyond and between my speakers does just the trick! When I position it right, it just livens up the sound so that, say, a wood block or drum snare is now slightly "popping" from the acoustic of the recording and now sounds more texturally present and "right there."
When I get this right it frankly feels a bit uncanny. On one hand I'm sort of enveloped the acoustic of the recording, but it's like I've "entered" that acoustic because now the sounds have a bit more "it's happening live in front of me" tonality and presence. So it's as bit less like the sensation of the recordings shape shifting behind the speaker but more the part of the room from the plane of the speakers is shape-shifting in to the acoustics of the recording. A sort of Star Trek Holodeck vibe. I've been fairly astounded at the sensation, with my eyes closed, of orchestral recordings where the sense of depth seems to go on "forever" in to the hall, and I can hear the hall acoustics so well that I'm peering in to, but the instruments in that acoustic sound more "live and happening in front of me."
This is the kind of thing that give me my audio/musical thrills. And it's why, per the question of the thread, I'm fine with speakers sounding different.
Yet I can completely understand why people take a different approach.