Ovinomancer
No flips for you!
Well it depends. It's going to vary by group. Verisimilitude matters more to some groups than others. For some, it doesn't really matter at all....so there is no stretching, and certainly no breaking. And please....I used Waterdeep as an example not an endorsement. But even still, my Realms may be exactly as "sensical" as any world you build....it's all up to interpretation and application. I use Faerun in my games, but I don't rely on any mechanics to establish my world, and the lore I use is pretty selective.
I honestly don't worry overmuch about the number of encounters per day, or meeting some arbitrary XP budget or anything like that. Sure, I recognize that individual encounters need to be designed a certain way in order to be challenging when compared to a series of encounters. I personally don't use random encounters very much at all.....even when I do decide to have an encounter come up out of the blue, I usually just decide what to have happen rather than consulting any tables. My world doesn't really have Random Encounter tables to speak of, to be honest, except if you consider the published material that I incorporate into my game and the tables that come with them. But I have not yet rolled on any such table while playing 5E.
So, for me, if the PCs are in a place that's safe....or even just safe enough that they won't have the kind of encounter or number of encounters to present an actual challenge....then I don't bother with having encounters at all. I narrate the trip. So there is no adjustment to achieve an "adventuring day" which then impacts world-building.
Another way I avoid this is by not having detailed encounter lists for areas. I think that such lists are as likely to hinder as to help. So I don't have them....so then without that, how do I determine if a few hard encounters are impacting my world-building? Not having a specific pre-determined list means that whatever I add, I'm not contradicting anything. I tend to rely on in world information to establish such information, and then use that as a guide for what can/will happen in an area. I don't commit that strongly to any such information ahead of my players knowing it that will make adding a specific threat a problem. Not unless the area in question is well known to be safe or dangerous or whatever.
So when I may decide how many encounters to have in an area....or if I decide to increase the difficulty of encounters...it's due to world-building decisions that I've made. Allowing the opposite to happen....choosing encounters that change my world-building....it just seems illogical to me.
You may be surprised to hear we do things in a very similar way, but then I also do hold to a static 3 deadly encounters a day, either. If I did, I couldn't place encounters while maintaining the authenticity of my game world -- it would break unless I built the world to accommodate it. And that was the totality of my point: dogmatic encounter pacing choices reflect back into the world just as much as the world reflects into encounter choices.
To say a different way, I don't see the world as static and unchanging and my encounter choices having to match it in frequency, power, and kind. Instead, I see encounter building as a function of worldbuilding -- it helps expand and populate the world idea I'm presenting. Saying that you can keep a static world while constantly adding things to it in the form of encounters sounds utterly alien to me, which is why the idea of a decision of 3 deadlies a day as a pacing mechanism (or any other dogmatic pacing choice) is obviously going to reflect back as the world I'm presenting suddenly becomes much, much more dangerous (because all encounters are more dangerous and because they run in packs of 3). How you can change the presented danger level and frequency of encounters without saying something new about your world is something I just can't grasp, either.