New (possibly) Initiative Idea

It's new to me, anyway. Here's how it works.
This is for basic fantasy combat, by the way.
Everyone rolls three dice for initiative at the start of combat, with results averaging between 10 and 20. The roll is recorded as the player's "initiative points" for the battle.
High roll goes first, then next highest, and so on.
When a combatant takes damage, the damage is first subtracted from these initiative points. In this sense, they are like "fatigue points." But losing them has the effect of actually making he character fatigued: he's acting slower, losing the upper hand in the battle.
When your initiative points reach 0, damage you take starts coming out of your hit points, representing actual wounds to your body.
You can regain one die's worth of initiative points for each round you spend doing nothing but catching your breath.
If you and your opponent both have 0 initiative points, you will take a breather round together, sizing each other up, the way boxers do. Then, after you've each regained one die's worth, you begin fighting again.
Here's what I like about the idea:
Getting a hit on an opponent can shift the tide of the battle. Let's say you were behind your opponent in initiative, but you score a hit that brings his initiative below yours. In the next round, you attack first, effectively getting two attacks in a row, which can tip the scales significantly.
It grants the players some hit points that refresh quickly -- even during a battle, if you can dispatch a foe and take a breather before diving back in.
Because it's rolled fresh at the start of every battle, it could give an underdog an unexpected advantage if he rolls high and his opponent rolls low. It's like the low-ranked team having a really good day against the favorite.
Even if you take a big hit to hit points, it doesn't mean you have to start the next battle at death's door. You've got all new initiative points the enemy has to plow through first. But it doesn't entirely undo the effect of damage, because once the new initiative points are gone, you will be easy to kill.
It puts initiative more on par with offensive and defensive skills in combat. Having a better initiative bonus in most RPGs isn't going to help a weaker fighter beat a stronger one, but here it could make a difference.
I can imagine leadership skills that might restore your allies' initiative in the midst of battle, rallying the troops, as it were. You grab the standard, blow the horn, shout the battle cry, and everyone on your side gets to roll a little bonus initiative die. It's a way of giving charismatic fighters a sort of clerical ability. (I'm always looking for ways to make clerics unnecessary. Sorry, cleric fans.)
So, is this already a thing in a game I haven't heard of? Is there a flaw to it that I'm missing?
This is for basic fantasy combat, by the way.
Everyone rolls three dice for initiative at the start of combat, with results averaging between 10 and 20. The roll is recorded as the player's "initiative points" for the battle.
High roll goes first, then next highest, and so on.
When a combatant takes damage, the damage is first subtracted from these initiative points. In this sense, they are like "fatigue points." But losing them has the effect of actually making he character fatigued: he's acting slower, losing the upper hand in the battle.
When your initiative points reach 0, damage you take starts coming out of your hit points, representing actual wounds to your body.
You can regain one die's worth of initiative points for each round you spend doing nothing but catching your breath.
If you and your opponent both have 0 initiative points, you will take a breather round together, sizing each other up, the way boxers do. Then, after you've each regained one die's worth, you begin fighting again.
Here's what I like about the idea:
Getting a hit on an opponent can shift the tide of the battle. Let's say you were behind your opponent in initiative, but you score a hit that brings his initiative below yours. In the next round, you attack first, effectively getting two attacks in a row, which can tip the scales significantly.
It grants the players some hit points that refresh quickly -- even during a battle, if you can dispatch a foe and take a breather before diving back in.
Because it's rolled fresh at the start of every battle, it could give an underdog an unexpected advantage if he rolls high and his opponent rolls low. It's like the low-ranked team having a really good day against the favorite.
Even if you take a big hit to hit points, it doesn't mean you have to start the next battle at death's door. You've got all new initiative points the enemy has to plow through first. But it doesn't entirely undo the effect of damage, because once the new initiative points are gone, you will be easy to kill.
It puts initiative more on par with offensive and defensive skills in combat. Having a better initiative bonus in most RPGs isn't going to help a weaker fighter beat a stronger one, but here it could make a difference.
I can imagine leadership skills that might restore your allies' initiative in the midst of battle, rallying the troops, as it were. You grab the standard, blow the horn, shout the battle cry, and everyone on your side gets to roll a little bonus initiative die. It's a way of giving charismatic fighters a sort of clerical ability. (I'm always looking for ways to make clerics unnecessary. Sorry, cleric fans.)
So, is this already a thing in a game I haven't heard of? Is there a flaw to it that I'm missing?