In terms of the math, this type of initiative system is much like achieving surprise: it can benefit you in the first round, but never afterwards. To see why this is, consider a simple initiative order with four entities, acting in the following order: A, B, C, D. Thus, assuming no entity is removed from the combat or delays, the actions would go:
- A, B, C, D, A, B, C, D, A, B, C, D, ...
- B, C, D, A
- C, D, A, B
- D, A, B, C
Given that, why not just let the character with the highest dexterity go first, and then go around the table? For added impact, seat players around the table in order of dexterity score (or initiative bonus, if you are playing a game that uses such a thing). The referee could use a Holmes-like system and roll 3d6 for monster dexterity at the beginning of combat, and then have a roll-off to determine if the cycle would start with the monsters or the PC with highest dexterity (the advantage here is 2 rolls per combat rather than N rolls, and no need to write down the order or bounce around the table).
For comparison, it is also worth mentioning the AD&D/segment "count up" system, which is similar to, but more elegant than, the d20 system. In the "count up" system, everyone rolls 1d10 and then subtracts their dexterity bonus and adds things like casting times and other penalties. The referee then counts up from one until every entity has acted (thus, lower is better). The advantage here is that weapon speed factors and individual dexterity can contribute to the order of actions without needing to write down an initiative sequence. Since everyone tracks only one single number, it can even be rerolled every turn, so that characters with quick weapons or high dexterity scores will go first more often than not, but nothing is guaranteed (making combat more interesting and less predictable).
It seems to me that the d20 style of initiative is a clear example of a misapplied core mechanic. Roll a d20, higher is always better just doesn't seem to be convenient for the problem of determining initiative order. I'm probably missing some subtle awesome stuff that can be done with delaying actions in the d20 system. If so, please enlighten me!
Personally, I am quite happy with the Moldvay D&D method of rolling d6 per side every round (I even used that system with Fourth Edition), but I was thinking about this and just wanted to get my thoughts down. The dexterity bonus is only applied to initiative rolls in Moldvay for one on one combats; otherwise, it is a d6 roll unmodified by any character stats.