Strictly No, but there are advantages at modestly high ability scores that could inspire your DM to add more
There is nothing explicitly in the RAW (rules-as-written) to give a "yes" to your question.
However, we could note that the RAW does specify some advantages for higher-than-average ability scores. Some heavy armor requires Strength 15, and some feats such as Defensive Duelist, Grappler, Inspiring Leader, or Ritual Caster require an ability score of 13.
So if your DM uses feats, then it would be reasonable to ask your DM to add feats with even higher ability score prerequisites, thus creating some form of a "Yes" to your question, when it comes to how your table is run. Nothing stops your DM from creating feats that require, say, a 15, 17, or even 20 in an ability score, though this is not terribly common.
Furthermore, Xanathar's Guide to Everything puts forth specific benefits for having passive Perception of 20 or 15:
Whispers don’t disturb sleep, unless a sleeper’s passive Wisdom (Perception) score is 20 or higher and the whispers are within 10 feet of the sleeper. Speech at a normal volume awakens a sleeper if the environment is otherwise silent (no wind, birdsong, crickets, street sounds, or the like) and the sleeper has a passive Wisdom (Perception) score of 15 or higher. (XGtE)
Again, this is just support for requesting that your DM consider making a house-rule or a homebrew feat.