Initiative by weapon priority

I've been looking for an initiative system for my nascent OD&D game, and came across the weapon priority charts on page 17 of the Judges Guild Ready Ref Sheets. I'm not positive that those charts were originally intended as an initiative system per se, but they could do the job. This violates my general principle that any house rule should be expressible as a simple sentence, but something about it appeals to me—perhaps that it solves the initiative problem while giving players significant tactical options with low rules overhead. The original charts assign a weapon priority based on the type of attack, the armor class or monster speed, and the dexterity of each combatant. Three variable is a little too crunchy for my tastes. I don't think much would be lost by dropping the armor/speed and dexterity variables, and assuming that all actions of a particular type take effect simultaneously. This list is a slightly modified form of the Judges Guild chart:

1. Gaze attacks
2. Breath weapons
3. Spells level 1-3
4. Missile weapons
5. Long weapons (polearms, spears)
6. Spells level 4-6
7. Medium weapons (swords, maces)
8. Short weapons (daggers, saps)
9. Spells level 7-9
10. Read scrolls, other actions

Of course, you could still roll initiative to see who goes first at each of the stages—if that's your thing—or let those wearing no/light armor or with high dexterity act one step sooner.