Just out of curiosity, do you know what "slice-of-life" is? Like, do you understand the concept?
I don't know if it is a tag used in western media, but just a quick look on a single website shows this
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5,362 manga title, not single volumes, TITLES. As in there are, on this one site alone, over five thousand stories written by professional writers that are, by your definition... not stories? Because an active manga title isn't put together after the fact. But a slice of life story is
literally a story where the characters are just people going through the world and making choices.
They also have some of the most popular non-shonen titles out there.
I would say the main differences between "Slice of Life" and a story-focused TTRPG are:
The former are "ordinary" and rarely have climactic events; TTRPG chars almost always begin or become extraordinary and face many climactic events over time
The former rarely have "villains" and don't even need antagonists; TTRPGs almost always have villains and always have antagonists
SoL stories (I wish it had a better acronym) don't usually have dramatic
arcs so much as "popcorn"-style events; a story-focused TTRPG almost certainly plays out arcs, they're just done "with" the camera frame, rather than before or after it
But there certainly are similarities. One might say that "Slice of Life" follows the action as it happens, so to speak, which is definitely what a "story now" RPG also does. Further, "Slice of Life" embraces a spontaneity of behavior and growth that a more rigorously plotted story wouldn't, which is very much true of "story now" RPGs.
The closest analogy I can think of for the specific kind of story that "story now" RPGs produce is Choose Your Own Adventure, except that CYOA narratives are completely fixed (y'know, being a written down
book) while "story now" is inherently open-ended both in terms of length and in terms of the actions you can choose to take in any given moment. Sometimes, only a few actions make sense (that's the fiction limiting your options)
It's not for me as the DM to decide. It's for the player's with their actions and the dice.
Given the DM controls the world, and thus what is in it, it is also your decision whether to intrude or not. Just as the DM always has the nuclear option of "rocks fall, everyone dies" or the equivalent, they also have what one might call the "pacifier" option of declaring that something
bad doesn't happen because Reasons.
Now, to be clear, I agree, unreservedly, with anyone who says that a blatant and ham-fisted "pacifier", a kludge that sticks out like a sore thumb, etc., is bad and should be avoided in nearly all circumstances. I'm just not talking about that particular kind of intrusion. I'm talking about one that does the work to be diegetic (whether in advance, e.g. "I planted these seeds and now they can flower two, twenty, or two hundred sessions down the line", or as an improv "I'll fill in the details later" story hook), that uses the least-intrusive means possible to achieve the desired end, and preserves continuity and groundedness as much as possible while still accomplishing the goal.
It's been rather frustrating, fending off complaints that effectively amount to "well you CAN'T intrude in a way that is diegetic, minimally-intrusive, and grounded" because...yeah that claim is simply false. You can do it. It isn't even that hard, and many games (not just D&D) do quite a bit of heavy lifting to simplify the process for anything except "low level" characters or the equivalent (e.g. low-karma chars in Shadowrun).