This ability is an ante *down* if anything. As much as I love the idea of a last resort attack, this thing has too many downsides! In your example you inflict yourself with 2 exhaustion (disadvantage on ability checks and halved speed) as well as making everything automatically deal double damage to you. All that for 12 damage plus a modifier. Might as well just use 1 ki point for flurry of blows and deal more damage with no downside...

This is either extremely strong or hilariously weak.

First off, if you ever use 11 or more ki points on this ability, you instantly die afterwards. I can see this being cool and cinematic in some contexts, but there's also the potential for abuse. Since there's no more downside to using 20 ki points than there is to using 11 (besides the ki points spent), you can just use this ability at max power, then have the party cleric cast Revivify on you. Not reliable, perhaps, but could take down a boss in a single hit quite easily.
The example given is poor because you would never use this ability on a basic unarmed strike. The text doesn't make quite clear what's valid besides a "single strike". So clearly no Flurry of Blows with every hit x4, and presumably also not the insta-kill ability fail of the Way of the Open Hand. But what about Way of Mercy's ability Hands of Harm? With one hit, the basic damage is 1d[4-12] + Dex + 1d[4-10] + Wis, which could strike reliably for a minimum of ~ 8 damage by 4th level, and likely much more; with a x 6 or 7 multiplier this becomes a 1/day hit for AT MINIMUM 50-ish damage. At level 4! Sure, you gain 3 - 4 levels of exhaustion, but typically the boss will be the last enemy you have to fight in a day, and a 50 damage strike will likely cleave the hitpoints of a boss intended for lvl 4 characters in half.

You thought that was it? Not even close. The Way of the Ascendant Dragon has a 3rd-level ability that allows you to replace an unarmed strike with an area effect for 2d[4-10] damage. Since it replaces an unarmed strike it seems like it fits the conditions of the feat. Now you can annihilate the boss' minions as well! If you wait til 5th level, this ability deals an average of 2d6 = 7 damage, which multiplied by 7 is an area effect for almost 50 damage. Strong, but not even so terribly broken - casters get Fireball at this level and that deals about half as much damage with no downsides. 

Where things get very interesting indeed is with Way of the Four Elements. Disciplines like Fist of Unbroken Air and Water Whip can deal 3+ d10s of damage at the cost of some ki, and use the word "strike" in their discription, and are therefore presumably valid targets for this feat. For 2 ki points, you can strike a creature using one of these for 3d10 damage (average 16.5), which with even just a x4 modifier is 66 damage! This will easily take out many 6th-level boss, and can continue to decimate single targets for most of the levelling.

The downsides are also so crippling that there is no other valid time to use this feat except on a final boss. Halved damage dealt and doubled damage taken will effectively take you out of the fight (if multiple levels of exhaustion don't do that already) and there is also no time specificied for these effects to end. Presumably this occurs at the next long rest, but it is not made clear.

Here is a version I made which fixes these problems (although it may create some of its own, feel free to comment & criticise):

Last Resort Strike
Prerequisite: Monk

You can empower your strikes to annihilate your foes when you most need to. When you hit a creature with an unarmed strike or monk weapon, you can spend a number of ki points (up to a maximum of 6) to enhance the power of the blow. For each ki point you spent, the damage of the blow increases by two rolls of your Martial Arts die, and you can cause the blow to deal force damage. You then fall prone, and gain a number of levels of exhaustion equal to half the number of ki points you spent (rounded up).