If I got to choose any initiative system, I would choose the card based one from Savage Worlds....still my favorite aspect of that system.
The cyclic initiative is simple and I think it fits D&DN design goals.
But if it was to change, I'd suggest a radical idea: get rid of initiative entirely.
What I mean is:
1. Everybody declares their actions. Declarations can be changed until everybody is satisfied with theirs.
2. Everybody rolls for their action.
3. Actions are performed from highest to lowers roll result. Actions that are no longer valid at the point of their resolution are ignored.
This way, your roll decides the success of your action - and it includes the timing. No need to separate initiative from action itself.
How does that one work?
The cyclic initiative is simple and I think it fits D&DN design goals.
But if it was to change, I'd suggest a radical idea: get rid of initiative entirely.
What I mean is:
1. Everybody declares their actions. Declarations can be changed until everybody is satisfied with theirs.
2. Everybody rolls for their action.
3. Actions are performed from highest to lowers roll result. Actions that are no longer valid at the point of their resolution are ignored.
This way, your roll decides the success of your action - and it includes the timing. No need to separate initiative from action itself.
My friend recently told me about the initiative system in the new Marvel RPG. Basically the players decide who goes first (the GM may optionally choose one of their charcters). The player whose character went first chooses who goes next. It could be another PC or it could be an NPC. And it goes down the line until everyone's had a turn. The purpose was to easily facilitate teamwork between superheroes but maybe the same could work for D&D.
From what I can google, it's cyclative, but you draw cards instead of rolling dice.
The cyclic initiative is simple and I think it fits D&DN design goals.
But if it was to change, I'd suggest a radical idea: get rid of initiative entirely.
What I mean is:
1. Everybody declares their actions. Declarations can be changed until everybody is satisfied with theirs.
2. Everybody rolls for their action.
3. Actions are performed from highest to lowers roll result. Actions that are no longer valid at the point of their resolution are ignored.
This way, your roll decides the success of your action - and it includes the timing. No need to separate initiative from action itself.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.