So to get back to the point: Yes the solution is to appoint someone a magic arbiter, and hope they don’t screw up. The fact that it’s a deeply imperfect way of solving problems doesn’t mean it’s not workable. It just means it will backfire at some point, and someone else will get appointed instead.
This is the heart of the matter. Nothing is good or bad in a vacuum, but when two things (say, outcomes) can be compared, distintions can be drawn. Noticing flaws in the present can't be contrasted with simple models of "the better solution"; this is comparing apples to oranges. Address both the good and the bad of the present, including the days where nothing noteworthy happens and therefore below the awareness of most people, and the good and the bad of an elaborated counterpart.
The reason none of this makes sense to me is that it's intellectually crippling Internet users. Computers and the Internet are tools. If you want something machine translated to you, you can use a tool like Google translate to translate it for you. If the webmaster does this, it robs people from the opportunity to learn to use those tools and they become dependent on third parties to do this for them when they would have a lot more freedom if they just did it themselves (or if they learned English).
Teach a man to fish...
On what do you base this assertion? I was not able to find up-to-date statistics, but 72% of participants in this survey from 2013 had internet access at home, either via PC or via mobile devices, and another 11% had internet access elsewhere:
https://digitalimik.gl/-/media/datagl/old_filer/strategi_201...
If this is true, then the easy solution would be to just have two separate wikipedia editions (assuming there is interest).
After all if we have en, sco, jam and ang, surely there is room for two greenlandics. The limitting factor is user interest.
That's... a reach.
An easier, and much more realistic, solution would be to just have one edition in Danish, which was already noted as the language Greenlanders have in common.