However, there is the other 20% of the time. How could dagger man possibly go first when he's got to cover 30' of ground and I've got a 9 foot spear?
This sort of thing always eats away at me. AD&D 2e even added Weapon Speeds, which gave lighter weapons, like daggers, better initiative--except that's not how melee weapons work! Reach is generally a more important factor than weapon speed when determining who attacks first in melee combat.
The only way a dagger wielding combatant could strike a spearman first is if the spearman was surprised or unable to bring their weapon to bear (maybe it got stuck in somebody else's corpse or they're fighting in tight quarters and there are too many obstructions). Otherwise the combatant with the longer weapon always gets a chance to strike before the one with the shorter weapon.
Weapon speed IRL doesn't even help you attack "first", It helps you attack
faster, improving your attack rate. Though, that's tricky to handle in TTRPGs, cuz giving light weapons an extra attack per round would be too much. Giving an attack bonus to the lighter weapon might be more appropriate, since faster attacks are more difficult to evade or parry before they reach an opening.
Order of actions by random initiative makes no sense and isn't even necessary. You could handle order of actions by GM fiat or by phases based on proximity and readiness--whoever is closest to their target and/or immediately ready to act goes first (ranged within range, melee already in melee, etc), whoever needs minor preparations goes second (move, draw/reload weapons, etc.), whoever needs lengthy preparations goes last (reload flintlocks or crossbows, etc.). PCs and enemies act at the same phase, and enemy actions get resolved at the same time as PCs attacking them, then any enemies who haven't acted yet after all PCs are done resolve their actions last in that phase.
The real reason some people want to roll initiative is cuz they've been conditioned to think in terms of wanting to "go first" so they can kill an enemy before they've had a chance to act. Which sounds reasonable, except that unless you shoot them in the head or decapitate them, a wounded (even mortally wounded) enemy should still be able to make one final attack before they succumb to their wounds, and people killing each other roughly at the same time is a plausible scenario that does happen in real life.
Even if you want to go "first" to interrupt a particular enemy or make a called shot to the head you could handle "initiative" individually as an opposed test between adversaries (which used to do when I started handling order of actions by fiat or phases) without basing the order of actions of the entire combat around random initiative. OR you could skip initiative and say that if your attack succeeds by X amount (such as 4+ on a d20) AND you rolled higher than their attack or action (if applicable) you managed to strike before they could act, otherwise they still get an action before you kill or disable them.