In OD&D, where it is basically only a roll with a d6, initiative is not much of a chore - but not really much fun either. In other games which use individual initiative, it certainly gives more random and individualised results but also increases the book-keeping factor. It was argued by Justin Alexander that initiative, as is presented, does not function as a seamless way of transitioning from the previous game structure (hexcrawl, dungeoncrawl, or else) to the combat structure; furthermore, the book-keeping it requires weakens the dynamics the outbreak of combat would present to the players (see this post and this post with the comment).
Trying to solve these problems, I came across the new Marvel game which uses a turn sequence system that I find very clever: after acting, it is the combatant's duty to choose who acts right after him. There are two important restrictions: (1) you cannot delay your action, you act when you are called, and (2) nobody may act again until everybody has acted in the round.
The game leaves to the GM to determine the first one to act depending on the situation; in a D&D-esque game, I would say the one who states his action the quickest may act first. By instantly resolving the first participant's action, we - all of a sudden - find ourselves in the combat structure.
Opinions? What possible disadvantages you can foresee regarding this approach? Do you think the benefits proposed above outweigh them?