This is because you are trying to look at this as a distinct problem - solution instead of a conversation. Take a minute, step back. Look at the whole.
I asked originally "how do I make exploration and overland travel interesting with exploration challenges" and Iserith among many others responded with "Time pressure. Make it so they have to arrive at the location in time to stop the princess from being killed, this will prevent them from taking the safe path and lead to them fighting more monsters, which is an exploration challenge that is interesting."
I, after getting this answer a few times, pointed out that a ticking clock like this has issues. For one, the challenge of the time pressure fails if the party takes too long, you simply fail the mission automatically. Secondly, This doesn't actually provide new exploration challenges, it simply prevents solutions and forces the players to take otherwise unnecessary risks. Third, I have to manipulate events to make sure that the time pressure feels real, they have to be arriving just in time after their choices, or late and they fail. And finally, if I don't curate and manipulate the timeline, then I could have a situation where they arrive and blow through the climax, because there is no challenge if they arrive too early.
You stepped in and said that a lot of this was because I was given a binary clock. I have to make is a gradient. Add new monsters to fight at the climax for every day that passes until the clock runs out. I pointed out that still had most if not all of the same problems. Which is when you told me to remove the time pressure entirely.
The original premise, that the time pressure makes the exploration more engaging and makes for a better experience seems to be undercut if the solution to the issues of ticking clocks is to remove the clock entirely. So, it looks like, I was never actually given a solution at all.
And look, I get that no solution is perfect, but these aren't really minor flaws. The hard truth seems to be that not only does this involve gaslighting the players about the nature of the clock, but additionally at no point did anyone offer a real challenge for the actual journey.
You'll note that at the end of the post you quoted, I was actually saying that the princess and the cult when they don't want her dead is a great adventure. That has some real potential. The problem is though, that is the destination. Nothing interesting is happening on the journey to the destination, it is only after they arrive that we start engaging in the game and in something they will likely find fun. So, the part of the game I have been asking about, the actual journey, is best just skipped. Sure, keep track in vague terms of how long it takes to make the cultist hunting in the city more dynamic, but really, nothing interesting was happening on the way to the objective. That's the problem I've been trying to solve, and I'm trying to solve it without "throw more monsters at them". And it seems, we've now circled time pressures and shown they are somewhat lacking as a universal tool to make all exploration better.