While Star Trek
has many divergences from reality, it was one of the first science fiction television series that consulted at all with actual scientists and made even a partial effort to ground itself in realism. Its ground rule was to use real science as a starting point and diverge from it only as dramatic license demanded. It didn't always live up to that ideal, and few of the non-Roddenberry-produced incarnations of the franchise have made that much of an effort, but ST has enough foundation in reality (compared, at least, to most other mass-media SF) that it's worth the effort to try to connect it to real science and astronomy where possible. Yes, there are continuity errors that result, but there are continuity errors throughout the franchise pertaining to all sorts of other subjects.
It was never claimed that Earth was at the center of all four quadrants. On the contrary, it's simply at the border between the Alpha and Beta Quadrants, much as London is on the Prime Meridian dividing the Eastern and Western Hemispheres. Said border is defined as the plane which passes through both Sol and the galactic center and is perpendicular to the galactic plane.
Even before the quadrant system was devised in TNG, Trek was quite clear on the fact that the center of the galaxy was nowhere near Earth (see "The Magicks of Megas-tu" and ST V). So I don't know where you got this mistaken impression.
There are problems with making sense of any aspect of Trek continuity. But it can be an entertaining creative challenge to try. That's why we do it: because it's entertaining. That's what fiction is for, right?
I do applaud anyone's effort to do so. I recall an earlier pioneer towards this effort who had attended planetarium lectures and done independent research in order to determine the best fit for the Vulcan homestar. Ultimately it's wasted energy.
Exercising one's imagination and creativity is never wasted energy. Engaging at petty sniping at other people for choosing to do so, on the other hand, is definitely
First, let me clear up my statement, something which I though was pretty clear based upon prefacing it by stating "I do applaud..." which is showing positive acknowledgement for them attempting it, while I feel it is misdirected energy. That's what I meant by wasted energy. It isn't that the action is useless, it's that the effort doesn't seem necessary.
The Vulcan solar system is a fictional one, that was created in a collaborative effort in part by some established canon after the original series, but written by so many voices who naturally won't agree in any sense of unity, and written over more than forty years. That makes it all but impossible to say definitively that this star must be the Vulcan sun, because there's no way it can be.
The oddest aspect is using the Terran solar system as a point of origin given all of the races and cultures. Arbitrarily assigning Earth as being of more importance as a map reference point is kind of silly. The only reason to do so is some sense of pride and in trying to be authentic to canon. But to then do so, plus try to adhere to a Milky Way galaxy and match things up is mixing apples and oranges. If it's the centre, it's only a centre because of affectation and not because of stellar cartography.
It isn't logical. You can bet that the earliest known races who were spacefarers and became Federation members didn't use Earth as a point of importance. Do you think Vulcan or Andorian maps looked anything like that? Both had warp drive far before the Terrans, with the Vulcans being an interstellar race around 900 BCE and with warp capability ~ the time of the Roswell Incident. Their maps surely had quite a bit of difference from anything being discussed.
It's not wasted effort in the respect that it has no value. I would never say that because all of us have individual passions. I myself am creating stellar maps so people can find entertainment within the realm of Star Trek for a mod for GalCiv2 (something you can partially see in my signature). I've spent hundreds of hours doing so, and while that produces no economic benefit, it's purely selfless so people can have fun and use their minds in a strategic computer game.
I simply don't think we must make it match up. It just won't because as we learn better astronomy there will be planets detected and should we have assigned a Star Trek planet to a specific real Milky Way solar system that is absent the same characteristics, then that time will be "wasted" because there's no way to get it accurately.
It's fine if the stars and planets and nebula and other celestial phemomena of Star Trek doesn't match up with the Milky Way.