Time pressure (or consequences in general) is a big thing, so let's stick with that.
The DMG says that a party can move 300 ft. per minute at a normal exploration pace, or 200 at a slow one. In the 60 minutes before I roll and random encounter check, they will have been, looted, and gone home for a long rest.
There are some more practical exploration rules in the DMG, but it lacks any unifying procedures to hold them together. What exactly triggers a roll for encounters, or weather, or whether a monster notices a PC? The final playtest actually had a bunch of this stuff, but they removed it. Important procedures are missing.
Outside of dungeons, I don't think the game has any comparable procedures, either. OK, so the evil duke and his scary knights are trying to track down the PCs and their friends in the city. The PCs are racing against time to find a solution. How close is he to getting them? How do I decide when this happens? Do the players have a right to know how near he is, or that he is after them at all?
This is what I mean by incompleteness.
I'm still failing to see what procedure you would want or how it would work. Time pressure can work in multiple ways, it can be anything from the distraction you planted should keep the dragon out of the lair for the next 45 minutes, you took out some guards and if they don't check in within the next half hour the alarms will start ringing, you know reinforcements are likely coming and will be there by morning. The time pressure can be so varied, the scenario being played out can be so unique that I don't see how or why you'd want one standard procedure. There are many times I don't want my players to know the exact countdown because the PCs would not know. It's part of the fun. Did the distraction really work? Are the guards really that punctual? What happens if the info you have is wrong and you find out that the reinforcement will actually be there by midnight?
Related to that, if some of this is based on previous challenges or intelligence gathering, how well did they do? On a scale of 1 to 10 did they get a 1 or an 11 because they were more clever than you had expected?
It's that kind of flexibility that I want in a game and I think it's the kind of flexibility that the game encourages. Anyone who has watched spy movies, played any number of video games has a general idea of the kind of things that can and do go wrong along with how careful planning and intel can help out. The last thing I want is a metagame conversation at the table "Okay folks, this is round X of exploration so we only have 3 more rounds of exploration before we hit that random monster." It would take much of the sense of immersion and discovery out of the game for me.
Which was one of the issue I had with skill challenges as presented and used. We knew we needed 4 successes before 2 failures. There was no circumventing the hard-and-fast procedure, not clever ploy, no rabbit I could pull out of a hat. Any kind of procedural dungeon delving would start to feel the same.