Why is Dex associated with Ice instead of Lightning?

It's certainly not an oversight - each attribute is associated with an element, and this has been part of PoE's design for a long time.

Strength relates to hitting harder than others, and is associated with fire - which causes more damage, and is thematically associated with large-scale but not ill-controlled damage.

Dexterity relates to being faster and more accurate than others (which requires control), and is associated with cold - which slows enemies down, and is thematically associated with control (such as the phase "keeping your cool" - something which would be required to keep up a barrage of accurate attacks).

Intelligence relates to hitting smarter than others (getting more critical strikes, mechanically), and is associated with lightning - which rewards getting multiple critical strikes by stacking shocked, and is thematically associated with burst damage.

Slowing enemies down is part of the dexterity thing of being faster than them, and cold damage directly relates to that. Lightning has no specific relation or interaction with dexterity at all.

I can see where you can make an argument that lightning is fast, but lightning is also lots of things other than just fast - uncontrolled and unpredictable, unreliable (never hits the same place twice), and so on - none of which are particularly good matches for dexterity, which is about fighting with control and finesse.
In the end, all such associations are, of course, arbitrary to some degree - the associations which are part of PoE's design are of course not the only possible ones - I personally feel they make plenty of sense and are perfectly reasonable, but your mileage may vary.

On the note of "poison", I don't know for sure, but I believe that "poison" damage is mechanically chaos because a) poison shouldn't be easily resisted with armour and resistances which are generally seen as protecting against outside attacks, and b) It wouldn't make sense for poison to be affected by energy shield. Chaos damage happily provides those features, and the "chaos" label is non-specific enough that "poisons" dealing chaos damage over time doesn't seem to far out-of-place.

To be fair, a lot of that is speculation on my part - the attribute -> element alignments were in the game before I joined the team (start of 2011), so that's just the personaly conclusions I've come to rather than necessarily being the reason for them.

Interestingly, while burn and freeze were in early, the "shocked" effect for lightning damage wasn't done until much later - there was a lot of discussion of what made sense for it to do which would be different from burn/chill/freeze. I don't remember anyone specifically mentioning that the stacking shock rewarding successive crits fit nicely with intelligence being the crit attribute (at least not to me), but when I realised it did a little while after it was added, I was quite impressed.