"Or, as you put it, why is it okay for base damage to differ purely because attack speed, but not for any other quantifiable effects to differ for the same reason?"
No, it is not okay for base damage to differ purely because attack speed. Does that answer your question?
There are a couple of rationales why attack speed would affect on hit effects. Imagine that the weapon has a capacitor where the effect is charged on to. Recharge speed and capacitor is dependent on the strength of the enchantment, the stronger the enchantment the faster the recharge & larger the capacitor. So say that you have a 10 damage/second charge rate on your weapon and a 10 damage capacitor. This would then mean that you could either hit once per second for 10 damage, after which every attack more per second would have partially charged on hit effect, so 5 damage for 0.5 second of recharge and so on.
Another rationale could be weapons size. Imagine that the on-hit enchantment requires a physical body to store the enchantment. Again like a capacitor for electricity. Having a small capacitor store as much energy as a larger one is more difficult, hence the same strength enchantment has a weaker per hit effect for a smaller, quicker weapon compared to a larger one.
And lastly, bigger weapons score bigger hits, allowing for more of the on hit effect to be transferred over. The better the contact on the target is, the better the on hit effect is.