Well, I emphasized fair, so we both agree on that.
Impartial though is a definite negative. Impartial in applying the rules is already covered under "fair and consistant" which I've championed. Impartial in terms of the rest makes for a worse game. Let me give a real life example.
I'm currently running two games with no overlap in players, both of which have been at similar character levels to each other.
One is full of veteran RPG players, mostly couples, aged 30s and 40s. They have a high degree of system mastery as well as tactical ability and I need to make sure that for their level the encounters are a lot tougher then the other group in order to keep it interesting. We have several players who really enjoy knotty RP and seeking allies or convincing people to help them, so I make sure that is a regular occurance. They like to "stay on plot", disregard side quests and aim for the big changes to the world, which I take into consideration when preparing adventures, but also like a good degree of autonomy in how they resolve them.
The other group is all full of new players. They are very attached to their characters and regularly do art and other things about their characters, including having longer backstories that they flesh out over time, including just hanging around and chatting about their characters. They get a little overwhelmed with too many plot hooks (I tried), and are better when there is at most two different hooks to follow. They enjoy down time, and some "slice of life" in addition to plot advancement, and also like a mix of important and side quest type things, as well as some deep and some light adventures in tone, unlike the hard-driving first group. After doing a number of exploration sessions, the player of the eladrin bard specifically requested some urban time she envisions a lot of scenes there for her character. They are very attached to their characters, with some getting distraught while at negatives, and did not have the system mastery or interest to build as strong combat-focus in characters or party synergy as the first group, and as such would not have fun with the amped up encounters as the first group, and it would likely lead to TPKs. They have all build characters with intentional flaws that they greatly enjoy RPing. They do regularly get themselves into trouble with those flaw, and that needs to be considered in adventure planning - they'd rather they have fun then their characters always succeed. Sometimes they also did not realize the mechanical effect of the flaws when building (even when advised), such as one person wanting to play an impulsive rogue with little common sense having a penalty WIS and failing a lot of perception checks that would be useful as a rogue. Or another multiclassing for a concept even though how they are doing it is leaving them weaker for a number of levels. Because building "maximum effectiveness" characters is not even on their radar as a priority.
Adventure building, session planning, and what to do next are highly based around the players in terms of skill levels, what they are interested in, and what they can handle. Fundamentally, they what they enjoy from D&D is weighted very differently and a one-size-fits-all approach would ill suit either group. In both cases I've changed focus on how I run for them since the campaign start, such as amping up the deadliness of encounters so they feel challenged, less sidequests, and big, important goings on for the main plot for the first group, and less hooks but more tonal changes in adventures including varying pressure, extensive down time, an urban homebase that they return to regularly and have some urban adventures, plenty of recurring NPC they develop relationships with, and scenario design around their play style.
Treating them the same would under the guise of impartiality or because I had a single vision of the world and campaign that didn't adjust to fit the players would be an active detriment to both groups.
This is showing great DMing. If you're not sensitive to the groups you're playing with, then it's like a director who doesn't bother to get to know his actors and what they're good at. He may still end up with a good result, or he may have big problems a result, but he's certainly not going to end up with as good as result as the one who does understand his actors is going to have.
I also find it interesting that some say the neutral arbiter cannot be a cheerleader or somehow, is at a disadvantage when it comes to creativity.
I blame D&D and its multifarious definitions of neutral, frankly!
The completely demented "true neutral" of early editions, where you have bizarre concept of someone trying to prevent "Good" being too successful (itself a senselessly symmetrical extrapolation from the Law-Chaos struggle of Moorcock) has sort of permanently warped the concept of a "neutral arbiter" for a lot of players, I think.
That plus the adversarial DMing of decades past. I mean, when I started, in 1989, adversarial DMing was almost seen as the default mode of D&D, well, maybe that and Monty Haul (which isn't even really the opposite, because I've seen adversarial Monty Haul before!). It's weird that in 2021, it's virtually a given that "be a fan of the characters" is the right way to do things, barely anyone would disagree. Because in the 1990s, they sure as hell would have disagreed (esp. in D&D - less so in other TT RPGs).
And there are certainly some "neutral arbiters" who are going to find it extremely hard to be a "fan of the characters", even based on what some people say in this thread. But like, you can let the dice fall where they may whilst being a fan of the characters, say. It's harder to honestly say that writing adventures whilst ignoring that the players and characters even exist is really doing that. It's not hard-antithetical to it but it's at least mildly adverse. Also I'm not sure this is completely true:
You can be a fan of the players, and their characters, while still being neutral in terms of action adjudication and consequences.
I don't think I quite agree. You can WANT to be a fan but sometimes you have to take an actively positive interpretation of things to genuinely be one. And I think 3.XE was really good for showing how this is the case. 3.XE, RAW, absolutely destroyed player attempts to so stunts and called shots and so on, by providing elaborate rules that amounted to calling for multiple rolls, often with high DCs, or serious penalties, if you wanted to "try anything clever". If you stuck to absolute RAW, and always gave the DC that seemed most correct (which was often pretty high), you would create a situation where it really didn't SEEM like you were actually a fan. Where it seemed, actually, like you were trying, by ruthlessly enforcing these "fair" (but let's be real - kinda crap for heroic adventuring) rules, to just really severely limit what players could do. And this exaggerated LFQW too, because magic didn't face the strictures, the same multiple tests, the same penalties to hit and so on. You cast a spell, it said what it does, so the imagination of the player was often the only limit, and very often there was no check at all (esp. out of combat).
But equally you could often ignored a few rules, or lowered a DC, or not made the penalty as extreme as some poorly-drafted and clearly unplaytested table said, and had a better effect. Would that make you "neutral in terms of action adjudication and consequences", though? I'd say clearly not.
Or look at 5E - you often have situations where you could potentially call for multiple rolls, when a stunt is being done (again this primarily impacts non-casters), or you could just make it, say, an Attack roll at Disadvantage, or one check and that (increasing failure chance of course but not as high as multiple rolls). And consequences are often in the DM's purview and pretending neutrality feels very fake. There's no rule as to what happens when the PCs try to con their way past the guards and totally fail. Someone who is genuinely a fan of the PCs and the players is likely to make something interesting happen, or re-direct the PCs, but not blow things up, whereas I've seen people trying to be neutral absolutely metaphorically crash the van into the wall there, because they felt it was "realistic". There's no rule to fail forwards, for example - but if you're really being "neutral in terms of action adjudication and consequences", without absolutely stellar design, you're fairly frequently going to hit places where, realistically, neutrally, the PCs would be somewhat stuffed - they couldn't go any further - they'd be at a loss. But if your adjudication was a little more generous, perhaps a tiny bit less "neutral" or "realistic", you might be able to provide a direction for them to go in.
So I really question this. I think you're kidding yourself if you think you can both be a fan, and completely neutral, esp. when it comes to action adjudication, where you control how difficult/easy something is, and consequences, which are often entirely DM fiat.