This is Very Unbalanced
The additional damage the Way of Mercy (WoM) Monk would be able to throw out with this would get absolutely ridiculous which would far outshine the Paladin whom is known for their nova damage. I think it's important to recognize, the Monk does already have the ability to deliver burst damage a lot of times per day by default, but it's usually via a lot of small attacks. But this proposal takes it over the top.
Assuming a 10th level Monk, you've got a character with 10 ki points for use. Given they're a Monk, they can regularly make 4 attacks per round using their Flurry of Blows (FoB). Given the Monk must spend 1 ki point to initiate the FoB, they would then spend an additional 4 ki points to trigger Hands of Harm. This would mean the Monk's damage output for the round would be as follows:
- 4d6 (base unarmed strike damage)
- 4d6 (additional necrotic damage)
- 4x Dex modifier
- 4x Wis modifier
This roughly converts all of the WoM Monk's attacks to deal damage which is worse than a crit because it also tacks on their Wisdom modifier.
But the question of whether this is unbalanced is still a bit nebulous, so let's quantify it. Let's assume the ability modifier is +4 for both Dex and Wis. This nets an average damage per round of 68; for comparison, without this feature triggering each hit the total average damage would be 34, so the difference is about 34 extra damage. Woof. That is straight up doubling their damage.
Given their amount of available ki, they'd only be able to pull this trick off twice and then need a short rest to recover. Assuming a normal adventuring day has 2 short rests in it, they'd see this trick being used 6 times in all. This amounts to about an additional 204 damage (24d6+120) per day. So instead of death by a thousand cuts, this monk deals death by a thousand necrotic motorcycles.
For the sake of simplicity, I'm going to forego discussion on the opportunity cost of this tactic. Obviously, if a WoM Monk elects to proceed with this tactic, then they can't do other Monk things like Stunning Strikes or Patient Defense.
For comparison, let's look at a 10th level Paladin and their smiting. At 10th level, they get 2 attacks, and similarly get to make the decision on extra damage after seeing if they hit. Let's give them a longsword and full spell slots (which is 4/3/2).
So each round, they attack with smites and their damage output is:
- 2d8 (base longsword damage)
- 4d8 (additional radiant damage from smite)
- 2x Ability modifier
Assuming a +5 ability modifier, the Paladin in this situation is dealing an average of 37 damage per round. They can do this trick once more before they expend their 1st level slots, but then they can start using higher level slots and dealing more damage. Overall, they can do this trick about 4.5 rounds per day, but due to the higher level spell slots, this totals an additional 112.5 (25d8) per day.
Similar to the Monk, a Paladin choosing to always smite will not have those slots for other Paladin things.
This means the WoM Monk can deal burst damage that is nearly double that of a Paladin focusing on the same thing. That is NOT ok. Even if it means that the Monk isn't doing anything else they're good at (Stunning Strikes), because they won't need to. The enemy is dead and pounded into a paste. What is there to dodge?
HOWEVER, then to make it worse, there's Physician's Touch, which says:
When you use Hands of Harm on a creature, you can subject that creature to the poisoned condition until the end of your next turn.
It is notable that there is no save on this. That just happens. For free. If you allow the WoM Monk to freely used Hands of Harm whenever they want, then they can pretty much impose Disadvantage on all enemies' attack rolls and ability checks on a regular basis. This means the need for the Monk to use Patient Defense goes away.
Coupled with a Monk's normal ability to quickly move around the battlefield (or just take the Mobility feat), this can get ridiculous very quickly as enemies who rely on attack rolls to deal damage will be regularly dealing with a substantial nerf which again has NO SAVE.
Enemies who can't reliably land their attacks are enemies who can't deal damage. And damage that's mitigated is damage that doesn't need to be healed. CR10 monsters are regularly dealing 65+ damage per round, CR5 monsters deal 35+ damage per round (DMG pg 274). Misses are very costly for them.
For this reason, I think being able to freely stack this condition on enemies can get out of control very quickly via a lot of mitigated damage, probably to the point of too much.
So you've got enemies whom are dead, dying, or poisoned after this Monk rolls over them. So yes, this is unbalanced.