Well, Random die (no stat) is fine for initiative...I wouldn't storm away from 5E in a hissy fit. However, I like the idea of having a character that reacts sooner due to inherent abilities.
I think Dex-based initiative assumes everyone "perceives" a combat has begun and is physically reacting to it. Being "Flat-Footed" fits this concept well. Two opposing patrols stumble out of the woods into a clearing. Everyone sees the enemy. The question is who shoots first? The best reflexes, that's who. Same in a gunslinger firefight. The Fight is a forgone conclusion.
In a Wis-based initiative (or int, but I think wis fits better), its not reacting to an obvious threat quicker, its about recognizing the threat in the first place. A great example is Han vs. Greedo. While certainly a tense and threatening situation, it was not a foregone conclusion that this was a case of "enemy! kill it!" and you had to have good reflexes to get the drop. Here, you had to perceive when the possible threat becomes a certain threat. Greedo certainly failed that wis-based roll (yes, Han shot first!)
Now having both types in the game might be a bit too much. But you could:
a) Have DMs ask for wis or dex based init checks based on the situation (ie characters have both)
or
b) Characters have one init based on class, such as dex for fighters and rogues and wis for Wizards and Clerics.
or
c) Characters Choose Dex or Wis based init at character creation.
I prefer a)
The wis cleric knows when talking is about to stop and the killing begins while the clueless fighter is still yawning over all the words. The Dex rogue reacts fastest to the sudden appearances of enemies in an ambush* while the wizard tries to dive left, dive right, and back up all at the same time before finally pulling out spell components, thereby reacting slower.
* as an aside, I prefer ambushers get a +10 to initiative when the ambushed fail a perception/spot check rather than a "surprise" round. A High dex, Improved Initiative Rogue may very well get the jump on the ambushers even if the rogue failed to spot them. While a very specific situation, its one of those things make initiative "fun" for a player when its actually based on the character build rather than a random turn order.
** another aside, initiative after the first round becomes essentially a static turn order (ignoring the delay or ready actions). This is where the argument for a simple static init is strongest. However, introduction of a mechanism to make Ready and Delay key off the initiative stat (dex or wis) or a new mechanism such as "fatigue", certainly makes things more interesting (as well as complex). Imagine spells or powers could move initiative down from fatigue.
At-will: no effect
Encounter: a 5-dex initiative drop
Daily: a 10-dex initiative drop
Haste Spell: a 10 initiative gain
Quicken Meta-magic: a 5 initiative gain on quickened spells
I know, complex, too much, whats the point. Not trying to write a new rule set, just pointing out *how* initiative can be made to matter after the first round.
