I don't see how one of these has to do with the other though. A DM can absolutely (and oftentimes should) plan out the details of the adventure area so that the PCs can research the info and have it at hand. I agree with your point on that 100%.
But that doesn't affect what the point of the "alarm time dice pool" mechanic is meant to represent.
Let's say (just for example) the party is going into that ruined temple at the edge of a freezing glacier on a snow-capped peak that you mentioned. They go through all their info gathering beforehand, and find out that there are many cold-based monsters within the ruins, and that the only real sounds that travel through the area are high winds.
Now... the party knows this and goes into the ruined temple. They encounter a small group of monsters in the first chamber and one of the PCs casts 'Thunderwave', causing this exceedingly loud peal of thunder that echoes through the temple. At this point the DM rightly points out that the spell was loud enough that its sound has probably resonated quite a ways into it, and its quite possible that other creatures in the temple have heard it. The players acknowledge that but decide to spend 10 minutes searching the monsters and the rest of the room for treasure. The DM says fine, and places a die on the table to let them know they've spent 10 minutes doing that action following the alert they gave off. Two further chambers in, the party comes upon a series of five corridors and spend several minutes checking tracks, checking traps, listening for movement etc. in hopes of figuring out which path to take. The DM says fine, and places another die on the table so that the player can know how much time they've spent thus far doing these activities since their alert went up. Then perhaps a way in the party decides to take a Short Rest, and the DM then tosses a few more dice into this pool.
At some point (however they decides to run this dice pool mechanic), the DM will pick up the dice and roll them in front of everyone to see what occurs (if anything). After that if nothing does, the DM will continue to put dice into the pool and continue to roll said pool after the times the party spends 10+ minutes of time doing stuff. At some point as the pool gets larger, the players would (hopefully) realize something is due to happen soon, and begin taking precautions or just stop wasting time. They don't know what is going to happen or when it is going to happen, but as time passes they know it becomes more likely.
Now, why do it this way (as opposed to say, the DM just rolling on their 'random encounter chart' behind the screen?) In my opinion, it is because it is too easy for players sitting around a table to forget all the stuff their PCs have done, because there's no reminder of it for them at the table. They're talking out of character, they're running to the bathroom, they're having snacks, they look at their phone, they're rolling dice repeatedly. All manner of things that takes them out of the headspace of what being in this silent frozen temple is supposed to be like. If they were actually IN that temple like their PCs are, they'd have constant reminders of what they've done. The memory of the Thunderwave spell would be ringing in their ears for probably several minutes. They would be on more constant alert. They'd hear the creaks and groans of the ice. They would feel the freezing cold such that they might be less inclined to stand around digging through snowpiles looking for gold.
Thus the point of the dice pool. A simple reminder that time is passing after some event has occurred that others in the fiction might have noticed. And the players can see the time passing, can know their actions have had a consequence, and can plan for when that consequence comes a-calling.
It won't be for every table or every DM. Many might find the dice too jarring, many will feel their own narration will suffice, many just don't feel the players need that knowledge or tension. Which is fine! No worries! But for those who might need something like this... having the option available as a mechanic can only be a good thing.
)
