There is a truth to BX being a cure for gamemaster burnout. In BX, the procedures for running a dungeon are very clear. You have a set dungeon turn, the referee tracks time and rolls for wandering monsters, the players track resources and interact with the environment, and the referee tells them what is around the next corner. Encounters are dynamic and fluid, with no preset script to read from, just a few ground rules about who they are, what is happening, and what the consequences could be.
But there is a structure here that creates the experience.
Modern gaming, like 5E or Daggerheart? We just jumped from the real sport of Greco-Roman wrestling to the WWE. Prescripted railroad adventures. Encounters with the story and outcome are prewritten. The dungeon has a story; the characters have multi-page backstories; and everyone and everything is telling a story.
We have moved from D&D being an unpredictable sandbox game to D&D becoming scripted professional wrestling. This is the single largest difference between classic BX D&D and modern D&D 5E.
Modern D&D replaces the BX sandbox simulation engine with a prewritten story you need to buy, read, and spend hours preparing to run. There is more money in fluff-filled hardcovers, after all.
And there is no game structure in modern gaming, just the prescripted flow of a story. Imagine playing baseball without any concept of innings, outs, or a set procedure of play. Imagine playing football without a strict timekeeping system or a division into quarters and halves. The teams get on the field, and just play the game until a preset outcome is determined, and the fans walk away happy since "everyone wins."
If you ran a game like that, you would get burned out since nothing really means anything.
Read the script, phone it in, turn off your brain; you are running a modern storytelling game.
And this sort of model is assumed for all modern games, where the rules exist to support an extensive story overlay required to even play the game. Pick up most games designed today, and you will see an overemphasis on story and very little emphasis on structure.
That gameplay loop and dungeon turn structure are the "sandbox engine" of BX.
And it is there to save a referee 90% of the work needed to run a game.
For the most part, BX runs itself.
Put a modern referee in BX, and wait a minute? What is all this structure? You mean, parts of the game that I had to write stories for and account for in each encounter automatically run themselves? And it is easier than hours of prep for each game, you just "hop in and play" and "the system takes care of the rest."
What is this game?
The game is BX, and the structures the designers built all the way back in the 1970s automatically eliminate the need for endless story writing before the game, and they allow any group to hop into a "dungeon environment" and have the story "dynamically generate." The same with wilderness adventures, there is a structure there, too.
Even if a referee had zero prep time, like homework was due and they had to go to band practice, that game could still be played. All the referee needed to do was "follow the procedure," and the game mostly ran itself, allowing the referee almost infinite room to be creative on the fly within that framework. A game could be run with zero story and no prep, and run just fine.
And what inevitably happens is that these story games adopt their own structure for story gaming and narrative flow, and that structure returns. Cypher System and its extensive narrative flow-control tools, and Daggerheart with its pools and dicing system, are examples of the structure coming back to "help referees," so you are not really getting away from structure; it has been renamed and moved to another part of the game (and likely less effective at running dungeons than the BX system).

The narrative dice in Star Wars and Genesys are another way to shift the structure to the dice for generic storytelling and are a touch fairer than other narrative gaming tools, since they are dice-based rather than at the referee's whim or tied to spending pools, as in Cypher or Daggerheart. Interpretation of the pool is still needed, but at least I am not feeling like I am "screwing my players" as I am in Cypher by triggering an Intrusion, or in Daggerheart by dropping fear on players. Those systems are more adversarial, whereas in Star Wars/Genesys I can point to the dice, shrug, and say, "bad luck."
My job as a narrative referee is a lot easier if I feel like I am not fighting my players. BX referees are a different thing entirely, and they enforce the game's structure at an event, with clear procedural rules. I am slowly shifting back to the narrative dice system of Genesys/Star Wars rather than systems like Cypher and Daggerheart, as they work better for solo play and clearly tell a story of what happens without referee intervention or bias.
As a referee, the more structure I have, the easier my job becomes.
The less of my own bias I introduce into the game, the easier my life is.
Structure cures burnout.
The elimination of bias and adversarial play makes the game more fun and engaging for the referee. These "screw the players" narrative trigger systems are ultimately fake tension, meant to be overcome anyway, and feel like throwing sand in the gears to create artificial tension and resistance to a predetermined story outcome.
With a sandbox system or narrative dice, the outcomes are not predetermined. Even the referee does not know what will happen. The next wandering monster check could kill the party. Rolling despair could mean a fatal wound, and that is the end of your character in one bad roll. There is no script. Your lives are at the mercy of uncaring, mathematical systems that have no care for your life or well-being, and you fight to minimize the impact of the cold, hard math of the system.
The story is how you deal with these impersonal, absolute, cold, hard systems during the game, together as a team. The story is never prewritten as a script before the play begins, cutting out all player input, and is doomed to be ignored anyway.
If you are burned out, tired of writing endless stories your players end up ignoring, and think roleplaying is "story gaming," give BX a try. If you are more of a story gamer, try Genesys and break free of the need to constantly oppose the players.
Let other systems do the work; instead of the game relying on you to constantly write reams of stories that will never get seen, read, or appreciated. Discover how great the game is without the need for all those scripts and massive, story-based railroads. Imagination happens during the game as a shared experience, not in hours of story prep toiling alone before it!
Immerse yourself in the structure.
Let the dice free you.
And discover the power of shared imagination.