Is the Ixalan Vampire’s Bloodthirst ability balanced around being used on downed enemy combatants?

For reference…

Bloodthirst

You can drain blood and life energy from a willing creature, or one that is grappled by you, incapacitated, or restrained. Make a melee attack against the target. If you hit, you deal 1 piercing damage and 1d6 necrotic damage. The target’s hit point maximum is reduced by an amount equal to the necrotic damage taken, and you regain hit points equal to that amount. The reduction lasts until the target finishes a long rest. The target dies if this effect reduces its hit point maximum to 0.

I’m a DM. I have a player who states that RAW, he can use this ability on knocked out (downed) enemy combatants at the end of combat for a 2d6 heal per combatant (and potentially 4d6 if they succeed their final death save on their turn). It’s his intention that with party teamwork, a large majority (if not all) of the combatants will be knocked out, allowing for fairly substantial free post-combat healing.

While RAW this seems to be the case, to me it doesn’t seem balanced. What are the opinions of other DM’s about the balance of this ability with this in mind?