It is widely believed that monks have too few resources, here's a house rule I made for my campaign's monk player. (Made in 1 minute)

Ki points should be per-encounter.

But I really really want to kill the "adventuring day" dead. I think a lot of players would have significantly more fun if it wasn't the core of DND.

The "adventuring day" is a relic of times when your entire campaign was exploring a megadungeon and you ran from one encounter to another, back to back, all night long. But barely anybody runs their game like that these days and the rules just never caught up with reality. Some people suggest having a constant time pressure on the party limiting long rests, and while it can work, it also puts a straitjacket on your story pacing where balance flies out the window if you ever let up on the pressure. "Guys, the apocalypse is merely hours away" quickly gets old when it's been that way for months.

Well, that and 99% of the rules involve fighting or exploring. Anything the rulebooks have to say on social interaction boils down to "well, you just talk to the DM, and sometimes they might have you roll a d20, just figure something out". D&D isn't really so much a role-playing game as it is a weird dungeon-crawling boardgame with some role-play elements. Sadly, people are allergic to trying new systems so instead they'll just try to bodge the one big-name king of TTRPGs, D&D, into doing things it was never built for, forever leaving them wondering why driving in screws with a hammer isn't as fun as they expected.
- I think the writers of Mage the Ascension got it best when referring to DnD as a wargame with role-playing tacked on top.
  
  So much of DnD the dnd rulebook and printed material is focused around combat and getting from one combat encounter to the next one.
Do you mean so it was balanced around encounters instead of rests? If so, yes please
Per encounter maybe with a bonus daily pool for short bursts of power that gets a partial refill on a short rest?

Widely believed? First I've ever heard of it. Do people not short rest or just run through all their resources in the first two rounds of combat?

Yes, the modern style of play is 1-3 encounters per day with 0-1 short rests. No more dungeons, go nova on every encounter
- This blew my fucking mind when I learned this.
  
  Nothing about the game's precarious balance works well if you don't follow the adventuring day.
  
  I push my players to the limit before they can take a long rest. If you blow your spell slots on stupid shit, you're probably going to wipe later. If you take five days to find the lost children, they'll be long eaten.
  
  "Do you want to play a game that's not a resource management game at its core?" "No we like DND"
  
  I need to stop playing DND.
- I can understand strongly limiting long rests. Letting players long rest between every encounter makes difficulty non-existent. Short rests though... classes that get resources back on short rests are balanced around the fact that they'll likely get them frequently.
- Yeah, that is so frustrating as somebody who plays a character that requires short rests. Our sorcerer throws out her 5th level spells every encounter and I have 2 spell slots as a warlock...
- Yeah, that's why I've started liking the idea of long rests are a week of rest, with short rests being a single night.
  
  Really makes the resources a lot more precious if you're not getting them back during the same session. So many times of players being like, "whelp, I just burnt five spells, let's long rest"
  
  What I should be doing is if you're long resting in the dungeon is having monsters show up, but I can literally see my players eyes glaze over when it's a random encounter like that.

Hear me out:

Double the number of Ki points. Double the cost of Stunning Strike.

Or: Monks have 3 stances: aggressive, defensive, and mobile. Switching stances costs a bonus action, and you can assume one stance freely when you roll initiative.

In aggressive stance Flurry of Blows is free.

In defensive stance Patient Defense is free.

In mobile stance Step of the Wind is free.

This way monks are not just a worse rogue, their basic abilities are now actual basic abilities.

That's very cool but DND will never have that kind of tactical depth without tying it to per-rest.

The adventuring day is garbage and it strangles cool ideas like this.
- It could be tied to per-rest. Similar to the fighters' weapon mastery in OneDnD, switching stances could be tied to a long or short rest instead. Just call it something else, like katas. (Yeah, yeah, they are trying to move the monk away from the strictly Eastern roots, but they could give this as a flavor option.) You drill one of the katas in the morning and then you can use the basic ability associated with it for free:
  
  Kata of the Wildfire: aggressive stance,
  
  Kata of the Mountain: defensive stance,
  
  Kata of the Zephyr: mobile stance.

The only resources a monk needs are his fists and feet. 🥊🦵

Doesn't help if those deal less damage than a regular weapon.
- That's why you get to attack twice right off the bat, but only without a weapon.

I think ki points should be wisdom modifier + proficiency bonus.

Not-thought-through 1 Minute Solution #2: Using the one higher die for Martial Arts from the class table (always d6 instead of d4, d8 instead of d6 etc.)