But you are deciding this... not the rules. You create or don't create the inconsistency or non-inconsistency of the world, not the rules. There are no rules that claim whatever the adventurers encounter... non-adventurers must also encounter. That's not a function of the game or it's rules that's a function of you choosing to make that so in your world. To do that and then claim it's affecting your worldbuilding is quite frankly silly... of course it is because you're choosing to build a world where it does... but the (encounter) rules of D&D in and of themselves don't force you to do that.
It may not be obvious, but I'm about to agree with you.
Fluff and crunch have to match up, or the consistency is shot. The crunch is that encounters happen X amount of the time. The fluff is that people run into orcs, dragons, etc. X amount of the time, where X is the same as the encounter frequency. If they don't match, the world consistency is off.
This is very much like the 'dissociated mechanics' kerfuffle. You had your choice of mechanics ('crunch') to model what your character could do, and the latitude to 'fluff' those mechanics in the narrative as you liked. It was only an issue if you willfully chose a flavor that didn't work for you.
Same thing, here, only it's shifted from the player to the DM and the character to the world (though, really, it's always applied to DMs on some level): you can let the mechanics imply what they may about the world, and not let it concern you, in which case the world will be consistent in that it always works according to the mechanics (though it might be decidedly Pratchett-esque), or you can change the mechanics to fit the level of consistency you want in the world, either way, it's only if you willfully choose to establish a fluff-crunch disconnect that you get an inconsistent world.
In both cases, the tools are there to avoid the 'problem,' it's just a matter of accepting responsibility for using them.
So, the only way to play is to provide encounters for PCs but never, ever consider how those might affect the broader world?
Not the only way, but a perfectly valid way.
So, then, if I make an encounter table that matches the PCs up against a Dragon (young), some gorgons, a pack of rabid manticores, etc, and then roll on it when they're walking from Peaceful Village along the Nevertrouble Way to Safeville, and tell the players that this is the safest area of the kingdom, then I don't have to do any explaining as to why all of these horrible monsters happen to occur to the players there?
They're heroes, heroes are trouble magnets...
... but, 5e went to the BA model, in part, so that you wouldn't have to resort to that kind of thing as much, or as dramatically. A more plausible encounter - bandits, a corrupt official and his guards, whatever - could still be non-trivial to a party of 'heroes,' you don't need to throw down a dragon (or whatever) just because they have some levels under their belt.
They should go, "Oh, it's a game...
It is important never to lose sight of that, yes. Not difficult, not a real risk, but important.
So you're purposefully choosing to place deadly encounters in the safest places of the gameworld because... why again?
Oh, because the original topic of the thread, and the 'solution' of using 3 deadlies/day: the story calls for a meaningful (possibly deadly) combat that day - maybe some sworn enemy of the PCs is going to ambush them or whatever, the world & the DM's vision/story, and the player's choices call for that to happen - but, it'll be a pushover and/or show balance cracks among the party if it's a sole encounter that day, so you need to attrit them a bit first, or present a plausible concern of encounters following it that they know about ahead of time to force them to manage resources even in a life-or-death struggle with a hated foe. It'd make 0 sense for the hated foe to divide his forces, so the other attacks have to come from somewhere.
So, throw in two 'random' deadly encounters.