On the other hand, you have the Monty Haul DM; this DM wants the players to be happy, to win, to get it all. DMs who want the party to succeed at all times because it's "fun" fall into this trap.
Ah I think this is attractive but ultimately is modernist revisionism and thus inaccurate.
I think you're back-projecting a 2020s take on to something that's been around vastly longer
I think this because have very clear memories of discussing and witnessing Monty Haul playstyles from 1990 to about 2000. Monty Haul DMs did not, back then, in the 1980s and early 1990s, "want the players to be happy" in
at all the same sense as "be a fan of the characters". This was trivially obvious if you met or talked to an actual Monty Haul DM. It was actually something much weirder, which was more like, he wants to
cheat the system, and hand reward to
his friends, which is not the same thing. You often saw this dynamic in Monty Haul groups. The DM was not a fan of the characters, but rather his friends and played favourites hugely. PCs in these sort of groups weren't invulnerable unless the DM was mates with that player right then. There was basically no such thing, back the '80s and early '90s, as a Monty Haul DM who just handed out loads of good loot to everyone (I mean, I'm sure at least one existed, but they were the exception, not the rule). Rather Monty Haul was about favouritism and sometimes an adversarial approach the rules (rather than the players) on the part of the DM.
This is why it was particularly distinct from the Neutral Referee, and is also distinct from the modern "be a fan of the characters" approach.
I do think it's important to note the "Cheat the system" (in the Robin Hood sense) and "reward RL friends" aspects when discussing Monty Haul.
I would argue that 5e is mostly set up to be a "soft Monty Haul" system. I do not mean that in the pejorative sense; it defaults to heroic fantasy, with incredibly high survivability, and the default that (at most tables) encounters can be overcome.
But that's just not how actual Monty Haul games of the era worked. They weren't heroic fantasy, they were power trips (often of a quite violently anti-heroic or even basically villainous nature), which are pretty different - this was major - I remember listening to players from Monty Haul groups list their achievements and best times in AD&D, and it was always, like gross stuff. Like killing a bunch of people (not monsters, people) in some flash way, or torturing NPCs, or being a brutal overlord. They didn't necessarily have "high survivability" either. Some were definitely softball yet others were pretty fatal, but either the victims would be non-favourites, or they'd be favourites who got to pass their entire loot on to their next character. Indeed I'd say the latter was absolutely characteristic of Monty Haul in those days - if your PC died, all their stuff went to your next PC. What we're seeing here in 5E is actually adverse to Monty Haul.
"Be a fan of the characters" is not how Monty Haul actually worked. Monty Haul's principle was "hand out cool naughty word to your RL mates
so long as they please you". So it's not "soft Monty Haul", even if you don't mean it pejoratively. There's a huge and fundamental shift in approach.
Both the Killer DM and the Monty Haul archetype are just exaggerations of the simple issue that most DMs had in navigating between Scylla and Charybdis; between the social pressures of a group game that is meant to be fun and played with friends, and the desire to "win" a game by taking an adversarial posture to the players. Both are just examples of the DM who is unable to avoid putting their thumb on the scale.
This is correct.
But in my experience, that's 100% of DMs, very much including every DM I've played with who claimed to be a "neutral referee". Maybe a DM does exist who successfully charts that course, but I am skeptical, and I suspect most who think they have are just letting Scylla pick off a few of their sailors and turning a blind eye.
In fact the "neutral referees" I've seen actually DM break down into basically two categories - but not quite the same ones:
1) "Mister RNG" - A guy with no ability to improvise, but a
lot of dice and a million notes. I don't feel like this is really "neutral refereeing", because the game would literally be better if this kind of DM didn't exist and a computer was running the same RNG/notes stuff. It would be much faster and more straightforward. This sort of guys is absolute nightmare when you go into a new area, because he's basically accessing the HDD but the HDD is him frantically paging through and scanning endless notes and rolling on endless charts (many of the charts will also create problems he then has to solve, too). I will say I haven't seen this guy since the early '90s, I suspect everyone who played in those games just went and played video games instead because the experience is overall better (and quite similar). Solo TT RPGs of the modern era prove this didn't even need to exist. To be fair I only ever saw two of these.
2) "Killer DMs who hide behind faux-neutrality" - This is the kind of guy who say they're a "neutral referee", but somehow the world they've set up is absolutely full of surprise deathtraps, gotchas, and NPCs who are extremely powerful and will kill the PCs for really any reason or even no reason at all! This was the vast majority of people I played with who claimed to be "neutral". They're very much in tune with the "I get out of bed" "Oh you forgot to say you removed the covers, so you get tangled in them and fall and take 4d6 damage" kind of DM - often they were the same guy. I would say most of them honestly believed they were neutral, though, they were just completely delusional about what actual neutrality would involve. Like some guy who fills his house with killer deathtraps, then invites a neighbour in, and when the cops are dragging him away, is shrieking about how he didn't intend to kill the guy and this was just an accident.
Pointless story time:
The funniest time I've seen Monty Haul/Neutral DM stuff cause an issue with in a university RPG society oWoD game in 1997/1998. There were multiple different oWoD games running, and The Powers That Be of the RPG society decided they were crossing over, whether we liked it or not (!!!), and thus there would be cross-table PvP (GREAT EVERYONE LOVES IT!!!). The Storyteller for the Werewolf game was absolutely full-on Monty Haul. All his mates at the Werewolf table had suped-up Grand Klaives and hybrid-breed garou and all this nonsense. I was but a mere high-generation (i.e. weak) Lasombra Antitribu "businessman" packing a double-barrelled shotgun with silver shot (mostly because the PC was a rich guy rather than because I saw this coming, because I did not). They brought in this supposedly "neutral" Storyteller who wasn't the Werewolf guy to run proceedings as the Monty Haul werewolves basically tore up my table of vamps, horror-movie style (oh the irony!). Eventually my PC got cornered in a library, but the guy playing the ridiculous three-breed (he even looked like a silly crossbreed dog, I know they thought it was cool/badass but it just sounded he was a very large humanoid Labradoodle or something) Monty Haul werewolf in question decided to go for maximum horror movie naughty word and just threatened me with his Grand Klaive and let my character shoot him, because what was I going to do.
When saw how many dice I was rolling (don't use "WoD: Combat" rules if you don't want trouble mate! You put the book on the table!) and and found out the shot was silver, then he completely failed his soak roll, the conferring between the "neutral" Storyteller, the Werewolf DM, and the Labradoodle garou's player was super-intense. I just sat there with a naughty word-eating grin on my face (my long-term smugness is marred by my memory that I was wearing an appalling late '90s "fashion tracksuit", god help me). Eventually they figured a way the Labradoodle could
technically survive, but that very thankfully caused them to end the PvP not just for that night, but for the rest of the campaign.
A victory for neutral DMing? I think not, but certainly a compromise was achieved!