At high levels your AC is better than most other martials. It tops out at AC 20, the same as a sword and board Paladin or fighter and they aren't dodging while they are attacking. At high level a dodging Monk is essentially a sword and board fighter with a permanent shield spell on herself who can also stun opponents regularly.
You won't take a huge hit when dodging, you will almost never take a critical hit and in addition to having good hit points, you have the ability to heal in combat while still attacking (although it is somewhat costly).
That's only if you don't take any Feats, or you managed to convince your DM to roll-up stats and got good rolls. Their AC
can be better than most, but that isn't really as true in practice because of the nature of the game. The Monk has to spend valuable ASIs, while others can simply put on armor. It can be better, but it certainly not always the case.
FOB is usually a waste of Ki.
Not sure I agree with that when the name of the game is damage output and certain archetypes have their powers tied to it.
Not very often in play. This is highly situational and rare. Keep in mind to use FOB you need to use it "immediately after you take the attack action", meaning you can not move between attacks like you can with regular martial arts. So that means all enemies you want to stun with FOB need to be in reach when you attack.
Uh, speak for yourself. Unless you are only dealing with mooks, the way health scales while damage only scales with extra attacks, I'm not sure how you
aren't going to be in reach of higher level enemies with time to spend on attacks.
Presumably if you are going to use stunning strike on your FOB, you are going to use it on your other attacks too. So for FOB to allow for stunning strike you either need 4 enemies within reach when you attack or you need a number of them to make a save such that you need that 4th attack to land a stun and you need to make this decision before you make your 3rd attack. This is not common at all, especially when you consider you are making the decision before the 3rd attack and you have to both hit and have the bad guy fail his save. Additionally if you have 4 enemies in melee reach it makes Patient Defense a much more powerful mathematically.
You don't need 4 enemies in reach, you just need one with a bunch of health, like a boss monster. The name of the game is damage output. Attached things like Open Fist stuff is useful as hell, especially if you have something like a Hex on someone's main stat and attempt to knock them down.
What Stunning Strike is really good at doing is burning Legendary Resistances or locking down someone who lacks those through sheer weight of numbers at high level. That sort of power is the reason you
have Legendary Resistances!
The fact you make this decision before the 3rd attack of the turn really complicates it as well. For example against one BBEG that you really want to stun - you get 2 attacks and 2 opportunities. IF both of those fail, well you still want to stun him, so at this point it is "do I try with the 3rd attack or do I FOB to get 2 more" - if you FOB here are the possibilities:
1. You use FOB and you hit with your 3rd attack and land a stun - FOB was irrelevant (to stunning enemy)
2. You use FOB and you don't stun him on your 3rd attack (miss or he saves) and you miss with 4th attack - FOB irrelevant
3. You use FOB and you don't stun him on your 3rd attack and you hit with 4th attack but he saves - FOB irrelevant
4. You use FOB and you don't stun him on your 3rd attack but do hit with 4th and he does save - This is the only time FOB did what you are talking about.
That is after you already failed to stun him twice with your attack action.
It is just a very rare situation that FOB will make a difference in stunning an enemy. What is more common is using it to get a better chance of killing a near dead enemy by giving you 2 more chances to hit instead of 1, but there too it often goes to waste as you hit with the first attack pretty often. It also can be relatively good at draining legendary actions to set up a caster, but that is rare too because you an enemy with a low Con save to be able to get 3 failures in 4 attacks.
I played a Monk end to end from 1st to 20th level and above 15th level she was the most powerful martial at the table. I used FOB very rarely, I think about twice the whole campaign. I used Patient Defense all the time.
I'm sorry, but this is overcomplicating the situation so much that I can't even recognize it as something realistic. I've both run and GM'd monks before and I've never seen this sort of thought process go into the use of Stunning Strike. Typically speaking it's a fairly easy call given the potential return on a fail,
especially if you have something lowering their saves like a Bane spell or Silvery Barbs (or Lathander help you,
both).
Like, your list of "failure states" misses that you have to get to those points to find out and trying to outlast up close with the Monk is dumb, especially if you are wasting Ki on dodging given how much To-Hit bonuses scale compared to AC: having a 20 AC is
adorable to an adult dragon who is adding +14 to hit you, even if you decide to Dodge. The whole point of the Monk class is to do things quick to overwhelm someone: I've seen a Monk hit someone with 3 attacks and only get a stun on the third one, but even still it was
massive because suddenly that creature can't do anything until the end my next turn, granting my allies advantage and the ability to do a ton of stuff.
To be clear you are making an active choice to dodge, not necessarily to tank. Dodging is a great improvement to AC, mobility and to dexterity saves, whether you are actively tanking or not.
You're making the decision to tank because you are removing most of your special abilities to move or shape the battle by doing so. If you are Dodging, you're expecting to take hits, thus "tanking" them. We're splitting hairs on words when we don't need to be.