When dealing with treasure, or monsters, or really anything, I prefer there to be intelligent design used - everything is there for a reason. That treasure is there because someone put that amount in there, not 'well the chest is locked and trapped but hey there's a silver spoon in it". If I'm fighting a monster I want the DM to have chosen that monster and that encounter, and not for it to be just whim. The same with DMing - I prefer to have a conscious choice and intention for everything. The PCs find that magic item because I intended for them to have it (but then, I don't believe in selling magical items, so things they will solves two issues with one move).
Chance is sort of the opposite, for me, of a Story. Sure, the illusion of chance is there, but it's not real. Randomness is chaotic and I don't like chaos. I've never seen anything "random" be positive at all. Order (or intentional design) is far more comforting and, IMO, feels more real.
The trick is intelligently designing the random tables. Roll a locked and trapped chest? Get a bonus on the treasure quality table, because it hasn't been pilfered yet so the good stuff is still there, and/or because people don't bother trapping valueless things (unless you're dealing with the cult of a trickster deity... which would be a perfectly valid reason to have a silver spoon in a trapped chest). If you don't like rolling lots of boring goblin encounters, don't put goblins on the table. Random tables and random encounters are a simulationist / gamist element of the game; simulationist in that they simulate the fact that the real world is reasonably random and unpredictable to one of human cognition (though if your PCs are truly Fated, then this is perhaps an unconcern), and gamist in that random encounters were, traditionally, an important part of strategic attrition, as discussed by the Alexandrian
here. When I build a random encounter table, I don't look at it as "Throwing some things together in case I'm out of material." I'm building a description of the inhabitants of a part of the world. The Random Critters Table in Traveller describes general trends in xenobiology across known space which are deducible in-game. Likewise, the Random Planets Table is a probabilistic description of an entire universe boiled down into a few pages (well, perhaps not so few), and which are similarly derivable by skilled planetary surveyors in-universe.
This is not to say that random tables aren't awesome for when I
am lacking in material; far from it. Occasionally the oddball result leads to really interesting things; "This planet has a beautiful, Class A starport, super-high tech level, and about 15 people living on it... How does this make sense... Aha! Homicidal robots, clearly. Or cyborg apotheosis to machine consciousness. Or a remnant of a dying, highly-advanced race. Or..." I find their ability to summon inspiration endearing. Take a random result, and embellish it. Run with it. Sometimes it goes off beautifully, and the players have no idea it was random. Sometimes it flops, but players tend to be forgiving in this regard as long as they get what they want out of the game.
As for intentionality... When I DM, I don't have that much intentionality. There are NPCs in the gameworld with intentions, and the PCs have intentions, but I as DM, Arbiter of the Universe, generally try to avoid having plans, plots, or intentions. I prefer to have a knowledge of the game world, a sense of cause and effect within it by which I can arbitrate actions, and randomness as a fallback when part of the gameworld is unknown or contested, or when the consequences of an action are unforeseeable.
In short: I agree with you that random tables are quite counter to planned narrative. As I prefer emergent narrative rather than planned, I find this non-problematic, and use them extensively for description of the world and for inspiration.
