Super-Simple Initiative for Large Groups

I was thinking about this last night as I was falling asleep. I'm sure someone's already come up with something similar, but here it is:

Step 1: Order PCs by their DEX score, then alphabetically by character name in the case of equal DEX scores. It works best if the players are actually sitting arranged in this way, with the highest DEX PC immediately to the DM's left, and the rest going down from there (clockwise around the table). If the players are already arranged at the table and this is found to be impractical, that's fine, just write the PC names down in the correct order.

Step 2: Assign a player to be the initiative roller. The DM will never roll. Each round, the player rolls a d6 with the following results:

1-2: Monsters go first this round, then the PCs
3-4: The first half of the PCs (the fastest ones) go first, then the monsters, then the remaining PCs.
5-6: All PCs go first, then the monsters.

You can modify this however you like, including a result for simultaneous action, if that's your thing. The PCs can be split into smaller groups, such as thirds or quarters instead of halves. The sky is the limit, but remember that the point of this system is that you shouldn't have to think about it much, and faster PCs still get the advantage of acting earlier.

The main advantage is that the PC order is never altered, so the DM can use the same list to check off which PCs have acted for the entire session. Anyone who's ever run a game with a large group using individual initiative as written in 3E/Pathfinder knows why this would be a great boon.