@deadlover
It's much easier to attain a neutral/accurate sound if your starting point isn't heavily colored to begin with. The main reason is this:
If the coloration is due to the inherent physical limitations of the gear, and you try to push it with EQ, the gear will distort because it can't handle the amount of EQ you're applying. For example, trying make cheap earbuds reach 20Hz, or even 30Hz flat and still sound clean, will be impossible because the crappy driver just can't handle it. The closer your starting point to neutrality is, the easier it will be when you try to EQ it.
And you're right, there is no clear point of separation between almost accurate and too colored, but that applies to so many things in life where there are no clear boundaries between many things. So what we are left with is simply to try our best and reach for the most neutral and accurate we can within our means.
When you say that your relative starting point is fixed, even if it's colored, that's just like saying if your TV has a noticeable green color cast all the time, but it's okay because at least that green is fixed and you'll still be able to spot the relative differences between colors. The question you should ask yourself then, is why would you want a TV that has a noticeable green cast to everything it displays? Why not have a neutral/accurate display so colors appear as they should?
Your example of the accurate gear and a track that is purposely mastered to warmness of 4 doesn't make any sense because it's illogical as an argument. If your gear is adding coloration, then it's exactly like a TV that's adding a color cast to everything it displays. If you enjoy that sort of thing, then by all means, continue to enjoy it. But most people I know prefer to have a neutral device that reproduces what it's supposed to without adding its own exaggeration. Imagine if you had a spoon that imparted its own flavor--let's say garlic, to everything it touches, whether it's ice cream, cereal, roast beef, or yogurt. Most people would much prefer a spoon that had no flavor of its own so they can taste different foods as they are supposed to taste.
If your gear is overall roughly +2 warm and you EQ it -2 warm to get it to sound more neutral, then yes, once you've done that, you could just leave that EQ alone and call it the day. That's basically what the ARC System is doing in my signal chain, and I have an EQ working on top of that to get even closer to the ideal neutrality.
In the case of badly produced music that's grating to listen to, those are isolated cases and most people don't have that problem. If you have a special interest in crappy bedroom music made by people who have no idea how to make a good sounding production, then that's your unique problem, and you can deal with it however you like. I have some songs in my collection that's a bit too bright or of low quality that's grating to listen to, and if I must listen to them, I often just add another band to the EQ and do a simple broad dip from 4KHZ to 8KHz by as many dB's as it takes to get rid of the grating harshness. It takes me about 3 seconds to do it, and when the song is over, I delete that band.
The Stax Omega 2 certainly is not something I'd call very colored. It's not quite neutral/accurate, but it gets closer than most headphones out there. I have EQ'd my Stax 007 mk2 and got it to sound fairly neutral, but even without EQ, I enjoy its sound enough to often listen to it without EQ. The LCD-2 is the same way, although it's a bit more neutral than the 007mk2 in general. The HD650 is also pretty good, except for the lack of authoritative sub-bass. It's harder for me to listen to the HD650 without EQ though, because I really need that sub-bass presence in order to feel like I'm listening to a full-range system. Even just watching movies or playing games, the HD650 doesn't reproduce the oomph in the explosions and rumbles to a satisfying degree.
I don't think anyone is saying you don't get to enjoy music as much as those with more accurate sounding gear, but what is true is that you are enjoying music that always contain the gear's unique coloration, just like a TV that has a distinct color cast or a spoon that imparts its own flavor to the food. If you find that enjoyable, then it is enjoyable. It's really a matter of preference. It just happens that a lot of people prefer their gear to be as transparent as possible and not impart its own flavor into everything they hear.
I find it a little amusing though, since from the way you write in your posts, one would almost assume you were defending low-end consumer gear that sounds really colored, but you are in fact using Omega 2, which is what most would consider to be closer to neutral than not in the headphones community.
BTW, I'm an artist, and I also teach art as well (you can check out my work at my site: www.ethereality.info). One of the most important lessons I teach my students is to learn how to convey exactly what they meant to say in their artwork so that their audience can understand what the hell they're trying to express. Believe it or not, most artists want to be understood, and they care very much whether their work resonates with people in the way they had hoped. Now if they think you're simply a shallow Rube who doesn't have the ability to appreciate their work, then that's a different story. In such cases, they are glad you don't understand their work.
Oh, and based on your description of "random Japanese high school girl singing," you might want to check out this girl who goes by the name "sundaytube." Search for her on yourtube and you'll find her. She's a multi-instrumentalists and singer, and she specializes in covering Japanese idols from the 80's. Really delightful voice, and she's quite a good musician with nice arrangement chops. Her early recordings were terrible--full of noise and distortion and very low quality, but she's improved her productions by leaps and bounds over time, and now sounds quite good. She just released her first CD recently.