Im not understanding the issue. Charisma 12 provides +1 to Persuade. Charisma 16 provides +3. If you are proficient, add +2.

So there is a big difference. A difficulty 15 Persuade roll will mean you need to roll a 10 or higher if you have Charisma 16 and are proficient. A 50% chance. A Charisma 12 with no proficiency means you need a 14 or higher. 30% chance.

As you get to higher levels, proficiency bonus goes up, so the higher the level the more your proficiency really matters.