I am not an expert for DnD 5E, but I know that for many CC spells the target has to make a saving throw every round to escape the effect, so the better your DC the higher the chance that it lasts long.
In DnD 2E the spell did not depend on stats of the caster, which means the chances of success got worse over time as powerful enemies have better saving throws.
You only had to make repeated saves for environment effects like clouds or entangle.
The same is true for 5e anyways. Yes, your proficiency bonus increases saving throw DC, however most high level monsters have ridiculous modifiers to saving throws, and most dragons have legendary resistance that makes them succeed at will. So CC spells only work against humanoids with stats capped at 20.