Ple-Sen
I tried to come up with a system with initiative and a formula for it:
Character's Initiative / 5 = action points.
Performing an action costs 1 action point.
If characters have the same initiative, the turn priority goes to the one who hasn't moved yet.
That is, a character with twice the initiative will move twice as often.
So, like in Heroes of Might and Magic V, for example? Or in Fallout, with the caveat that the formula is different there, and some actions require more than one point. Although, I suppose you'll also have some super-powerful abilities with preparation, considering that such abilities existed even in older systems. In fact, there was a similar system in the tabletop RPG, if I remember correctly.
With initiative, the main problem is that, if it's based on basic characteristics, you need to somehow balance the initiative characteristic relative to the others, as in many systems with this approach, such a characteristic is considered one of the most important, if not the most important. Even if initiative is the only advantage of this characteristic, it will still have a very high priority. It is also worth avoiding abilities that, for the same characteristic, will give you additional bonuses, so that it doesn't turn into Agility 2.0 from the old system, only even more broken. And if the core of the new system is old or similar to it, then it is necessary to make sure that the character's action points do not increase exponentially and the possibilities for increasing them are extremely limited. Otherwise, this will only exacerbate the problem of solo terminators deciding encounters.