If I were a Fighter, I'd hope to have a Belt of Storm Giant Strength by then...
If I was a Barbarian I would wonder why I didn't have a higher score.
If I were a Wizard I'd be wondering why I hadn't used books to raise my scores above that.
If I were a Cleric, I'd be wondering the same thing.
If I were a Rogue I'd be wondering why I hadn't used all my gold to retire as a rich man by that point, and be paranoid about other Rogues taking my gold.
It depends on what these ability scores mean.
For example, in my settings.
10 is average. 14 is extraordinary.
A 16 is something that most humans dont really come across day-to-day. There are stories about such people and their exploits, but they are often more like entertainment and legends.
18 is the peak of human possibility.
20 is superhuman. Because of magic (ancestry, fate, magical training, whatever), some humans are superhuman. But they are unique individuals in special circumstances.
Because tiers are important to set the tone in my settings, I like to keep the "apprentice tier" 1-4 (roughly college) moreorless like reallife. So a cap at 14 would help maintain this modest tone.
Then in the "professional tier" 5-8, some individuals come into their own prowess. But even then a score of 16 is rare, and life experience and dedication are part of it.
Scores of 18 and higher are non-normal.