If you have an offensive factor based on RNG, and you make the defense against it also random, the lower reliability means that the effect needs to make up for it in strength, otherwise people would just build Armor instead of Dodge. This is how balancing RNG works; because it's less reliable, it needs to be powerful on the occasions that it does happen.
Having the main defense against an RNG rely on separate RNG causes a binary issue in which it either activates and is an extremely powerful negation, or it doesn't activate and it was absolutely worthless. In the first case, the attacker feels powerless because there's little to nothing they can do about them dodging the attack (Sword of the Divine was worthless, don't even bother). In the second case, the defender is frustrated because they might have survived if they dodged even one attack, but it didn't happen.
And then, when you could get a higher Dodge Chance and it was activating more often than not, it would force them to buy a garbage item just so they might have a chance of winning a fight.
This was the reason that Dodge Chance was removed; it was either unreliable because it didn't activate, or overpowered because it activated multiple times and was the sole deciding factor of the fight.
And before you point towards Crit Chance, yes, some of these points apply to it as well. But the dividing factor is that Crit Chance has always come in higher percentages, especially after the Preseason patch. This makes it easier to hit percentage capstones such as 20% and 50%, which are more stable and consistent than 5% or 7.5% odds.
Now we come to the main point; what happened to the Dodge Chance items?
Well, look at them!
Ninja Tabi was immediately shifted from 12% Dodge Chance to 10% DR from basic attacks. In a world of perfect probability, that made it grant approximately the same defensive bonus without posing the issue of RNG activating over and over to provide a much higher effective defense.
Phantom Dancer took a breather, then came back with its own 12% DR effect as well, applying to all damage from a target rather than just basic attack damage. It not only gained a more universal defense bonus, but also switched from RNG to consistent defense.
From that, we can conclude that Riot probably wants more consistent defense factors in this game, instead of RNG defenses. While it's true that not all games follow such a model--as an avid tabletop gamer, I can most definitely point to a few dozen examples--we're focusing on League of Legends.