Multi-quoting here, I'll try to keep it brief.
I have to strongly disagree. I know both our experiences are anecdotal but I don't doubt within twenty minutes of a session probably sooner I would know the DM is winging it. So again, I don't doubt a good enough ad libber in theory, take God for example, could fool me. Those ad libbers are very rare in my opinion and I've yet to meet one. I've met quite a few that thought they were good at it though. It's why I mostly DM. I can't tolerate the slipshod job most other DMs put forth. It's also why I think I'm a popular DM.
So the question is -- how do I detect that the DM is making it up? Interesting question and I will make some suggestions but that is beside the fact that I am detecting it. If you had a pack of cards and secretly drew one and told me to guess, and I had a really high rate of success that fell well outside the bounds of normal chance then you'd surely suspect I had a means of detecting the card even if in all honesty I couldn't tell you how.
But here are some possible reasons
1. Lack of maps. Lack of diagrams, notes, etc...
2. Hesitation when NPCs are asked questions they ought to know.
3. Major hesitation or trite answers when questions about places farther away.
4. Inconsistent encounters, events, etc...
5. Lack of depth in NPC's motivations, feelings, connection to the world.
You've missed my point a bit. What I said was that you could really tell from the fiction that was generated. I'm perfectly confident that, in person or on a video/voice only line that you'd pick up on behavior cues that would lead you to your guess. The point, though, wasn't to say that improv can fool you -- I think this is a silly argument all the way around, the intent isn't there because the goal to fool you isn't there. That implies that not-improv is a goal, and so improv must be hidden!
I also think that a lot of your list requires trying to play in your specific way -- ie, theater of the mind pretty much dispenses with your 1, and can be prepped or not, so that's not a strong argument. The rest really can happen if I'm constantly checking my notes, or if I'm a tad disorganized with my prep (as can happen with a quick direction change).
Improver's,
I have no problem whatsoever with your style and your enjoying it. I do not want to stomp it out or in any way diminish its success.
I do though feel that you approach these discussions with almost a religious zeal. That if only we would see the light everyone would become an improver. This is insulting to those of us who are not. When someone says X is a reason and you say but we do X with improv, it seems you are trying to beat down those peoples defenses so they concede your way is the one true way. Let me say from many years experience there is no one true way. Fun is the goal and if you have fun you are doing it right.
Now as to player agency. I think player agency is the wrong term, at least for me it is. I'd rather say player challenge. Meaning that if my player is fleeing from the monsters having just recently lost a battle and finds an escape tunnel that was already there in the design (G2 Frost Giant Jarl) and escapes that is the stuff of legend in a group. If though that tunnel appears on player command, it's ho hum. Even if it appears 55% of the time on player command it's ho hum.
The players are wanting to defeat the monsters, traps, etc... by being challenged. They want to put their minds to the job of defeating the environment around them. So combats are tactical and decided mostly by how skillfully players use their powers and maneuver/flee as necessary. Dungeons are explored and treasures found based on how well the players engage the adventure. So that is part of it.
Now to a lesser degree, the players want that everywhere they go. If they need a cleric to heal the party and go into a town they want there to be a cleric there only if there was a cleric there. That means the DM prepped the cleric ahead of time OR the DM prepped that there was an X% on any given day of a cleric being in town and rolled that number. If the DM just says "Sure there is a cleric there" then that is a form of agency stealing. So a living breathing world is one where they know the DM is playing it straight (yes that is a degree of trust but that is just one part of it) and that the NPCs exist outside of the players purview.
So I apologize if in any way I am disparaging your playstyle. I do not intend to do so. People want different things out of their roleplaying. My responses of course represent my biases as do all of our responses. I actually enjoy hearing how you all handle things. I like other perspectives. I don't have to partake of every idea I hear but I like to hear of other ideas.
Okay, so, here's a truth: I'm currently running a 5e published adventure path. It's Descent into Avernus. It is prep heavy, especially since I make a good number of changes to the module to correct for things that would absolutely derail my group (the ham-handed railroad of the first chapter, for instance, would have seen open rebellion, so I had to make it a subtle railroad that appealed to them). So, yeah, I'm not zealous in the sense that I think people will play as I do when they realize anything at all -- I still play with heavy prep, railroads, etc.!!!
No, instead what I'm talking about is getting to the underlying reasons for preferences, because the ones usually given are hogwash. You might think that the only way to get a deep, believable, interactive, consistent game world is heavy prep, but this isn't the case. And, if you're arguing against any of the techniques that can do this without heavy prep, then your actual issue isn't deep, believable, consistent worlds! It's something else, and you should do yourself the favor of figuring that out, because you might find that you can get at that goal better with some small or maybe large changes. Or you might find you've already got it down and don't need anything more, but you'll be able to answer these questions more easily!
And, as
@iserith noted, you actually do this when you start talking about player skill in navigating the GM's key (shorthand). This is absolutely a worthy goal, and it is well served by heavy prep because heavy prep (theoretically) does the job of making a fair playing field that such skill can be deployed against. There are still other ways, and you might benefit from looking into them (I'd recommend how Torchbearer does this as at least a look -- it's not too far off from D&D, but it does do some new things).
Let's assume you are a master ad libber. Perhaps with everything being done perfectly on your side of the screen which I've yet to see but I will allow as a possibility since these forums tend to attract many who are successful paragons of their style, I agree it perhaps comes down to your thesis. But practically, many of the other objections while not theoretically implied are often very common.
Again, you assume the goal of a master ad libber is to perfectly recreate a prepped game such that the players can't tell in play. This is silly. Why would someone interested in an improv approach put in the work to recreate a different approach?
No, the point is, again, that if you read a story hour about each kind of game, you'd be really hard pressed to tell which is which.