I am also toying with capping the highest possible stat at 18 (16 for some races/stats as above), but increasing the Proficiency Bonus to compensate. My thought is that this will make certain characters really good at ‘their thing’ (i.e. fighters good at Athletics, Str saves, etc; Wizards good at Arcana, etc), but lessen their chances at things they are not proficient in. Just not sure about the math yet…
The current maximum is Proficiency Bonus 6 + Maxed Stat Modifier 5 = +11. Dropping to a max 18 score, a +4 modifier, max proficiency should be 7. Most easily, this could start with proficiency +3 at level 1.
You could also start with Proficiency Bonus 1 at level 1, and increases every third level: 1st: 1; 4th: 2; 7th: 3; 10th: 4; 13th: 5; 16th: 6; 19th: 7.
The problem with changing proficiency bonus, however, is that you also have to change all the monsters, because all use proficiency by CR matching the players. It's probably better to just cap the score at 18 and leave proficiency bonus as-is. The power difference can be made up through feats or magic items.
Capping at 18 also makes the Barbarian capstone even better.