This is why pbp is the way to go.
You have hours or even days to prepare for whatever random direction players want to run in, and there's always time to run to ENWorld and say "help, my players want to create an elephant-riding cavalry to storm the city walls!" and people here happy to help the DM with it.
No, you don't have hours or days. You're in the middle of running the game.
there are those DMs that it is near impossible to tell when they are improvising or when they have left their notes.
That may be because the quality of the game run by them with the notes isn't much cop either.

I take your point, mind you, it's just that in this arena, you must concede that computer games have the DM beat the vast majority of the time, unless he's an incredible improvisor, and they're so rare as to be considered an anomaly.
A simple DM tactic for dealing with things that you are not prepared for is to have a few generic things prepared so you can still run the game and let the players explore the new place after you've had a chance to prepare for it. Even ending the session early and let the players know it is because they choose something they didn't give the DM time enough to prepare for is okay. DM's have more options open to them then a computer game.
Only that's cheating. I'll assume you're conceding the point here - I'm not giving you a week to prepare between sessions, nor am I giving you a guarantee that we're still going to Lolrusland on the day. We might change our minds and head off for the Caverns of Ceilingcat. A computer will let you do that, and the Caverns of Ceilingcat will be fully detailed - whereas the vast majority of the time a DM would be severely compromised by such a situation.
I know the tactics you're referring to - if they want to go somewhere you're unprepared for, slow them down with combat until end of session, so you can prepare between sessions. That's the kind of cop-out I'm referring to which a computer doesn't need to do.
You also haven't covered the personal cost to the DM in having to prepare all this material for players on a whim. There's a
reason why railroading is the default for published adventures. Preparation for this kind of gameplay simply takes too much time unless the PCs broadcast exactly what they're intending well beforehand (which is, as I've said, cheating when compared with a CRPG), and pretending that computer games don't have DMs beat in this area isn't going to help.