You were right about how every Pokemon can have max EVs. However, the EVs still make a slightly noticeable difference. For example, let's imagine that a Pokemon gets hit by a special attack. Without EVs, the attacker has 126 special attack, and the target has 63 special defense. Damage is proportional to attack stat divided by defense stat, so the damage of this attack would be multiplied by two at some point. Max EVs increase each stat by 63, so with EVs, the attacker has 189 special attack and the target has 126 special defense. The damage would be multiplied by 3/2 instead of 2. The same logic goes for when the defense stat is higher than the attack stat. Basically, EVs make it so that differences in base stats don't matter as much.

source