This seems in line with an aspect of my original post which few people have discussed, which is that the HP result might help a DM determine something about the specific instance of a monster. If I roll a total of 7 hps for a skeleton, maybe it has been in a fight before and shows the cracks and scores of weapons on its bones. If I roll 19 hit points, maybe I decide there is a nearby source of necrotic energy that slowly but consistently "healing" or bolstering undead. Those are just off the cuff examples, but one thing I like about randomness in my D&D is how it can inspire me to include lore and/or crunch that makes it a more bespoke experience.
Yeah, absolutely, I like how you were inspired by that realization! Randomness is great for shaking things up.
I've been in the habit of modulating monster HP during my prep sine 2e, so it's instinctual for me, without needing to roll dice necessarily, "one of these goblins is the weaker one that gets picked on", "these wights are shambling and have half hit points", "the hobgoblins second in command has more hp than average", etc.
The issue for me personally is that random elements have to earn their weight. If I have 12 gnolls (avg hp 22) encountered nears ruins (until recently held by overzealous trappers/hunters) that overlooks rolling hills and a lake, rolling 5d8 twelve times and recording those results... it's not giving me enough back creatively for even that minimal effort to roll and record. If I were to...randomly rolling, one minute... get 17, 18, 20, 22, 24, 25, 26, 28, 28, 30, 31, and 36... for me personally that's not saying much I wouldn't arrive at on my own.
For example, without any of these rolls, I might decide one of the gnolls is at half hp (11) due to stepping in a hunter's trap, nursing its wound while the others cackle at its suffering. And I might decide the leader of the pack has maximum hp (40), with a wheezy advisor who has 75% max hp (30) and the ability to cast
augury by examining the entrails of a fresh kill. Ok.
Whereas, if we take those HP rolls, I might interpret them as... TWO gnolls (17, 18) are wounded due to stepping in hunter's traps... TWO gnolls (28, 28) are bodyguards for the leader equipped with battered bloody shields... one gnoll (30 hp) is the wheezy advisor... one gnoll (31 hp) is the ambitious second-in-command... and the leader has 36 hp.
The difference is slight enough that it's not really worth it (to me) to go through the exercise of rolling. I want randomness to influence BIGGER design moves upstream of the fiddly bits, if that makes sense.
Anyhow, that was my thought process behind my crazy suggestion to tie Hit Point rolls to other features of the monster - basically make the creativity well deeper.