Chaosmancer
Legend
What I've seen at the table is that the monk's higher movement, falling, ability to end charmed/frightened condition at will, and stunning strike get used in creative ways at the table to dramatically change the outcome of encounters.
A fun example was a monk in our group who grappled an enemy and dragged him off a ledge, taking no damage (I can't remember the exact height) then using his movement speed and a Ki point to quickly get back into the fight.
It's outside of white room analysis, but it brings something to the table that is (or can be) both more potent than "I do another 37 damage" and a lot more fun.
And I should probably add a disclaimer to every post in this thread that my experience is almost exclusively at Tier I and II. But if monks do need some love at those tiers, I'd prefer to see it be more of this kind of flexibility, and not simply more damage (although some more damage might be part of it). If I just want to do damage I can roll a Fighter.
So, I can see that, but all of those end up being pretty circumstantial.
For example, the "end charmed and Frightened" has a caveat. It takes an action. This means it isn't actually immediately useful against the Fear spell, because the fear spell says you must use your action to dash and get away. Which means your best case scenario is to dash, get out of line of sight. Next turn use Stillness of Mind to end fear if you didn't make the save for being out of line of sight of the enemy, then run and potentially even dash back towards the enemy, which could cost Ki or another action depending on if you can reach the enemy this last turn, meaning you are potentially looking at losing three turns... about the same as someone who failed the save and had to wait for the second save.
And for Charmed, I have heard speculation that the Monk needs to know they are charmed to take the action, which if the enemy has charmed them, and used persuasion to convince them to do something else with their action....
And the "suplex off cliff" is fun... but requires you to successfully grapple, and have a cliff nearby. And those sorts of drops aren't common, and not all enemies can be grappled. So, there are some niche scenarios that can be utilized, but I'm not sure if they are prevalent enough to account for falling out of step with the other classes. Because this isn't just "monks should be fighters" but a lack of increase in potential damage that even wizards and clerics have.