A tantalizing thought is brought up in this post: the personal use of the Psalms as indicated from the superscription.
We know that the tribe of Levi was scattered in many different cities in the territories of the other 11 tribes and was commissioned to instruct the ‘everyday people.’ Dt. 33.10: They shall teach Jacob your rules and Israel your law. 2Chron. 35.3: And he said to the Levites who taught all Israel and who were holy to the Lord. Neh.8.7b-8: the Levites, helped the people to understand the Law, while the people remained in their places. They read from the book, from the Law of God, clearly, and they gave the sense, so that the people understood the reading.
This was vastly different it seems from the wise men of Babylon and the Egyptian Scribes who were more centralized and served the ruler. Israel was unique in the ancient world in having more ‘everyday people’ know the Bible. To teach the people The Law the Levites needed copies of it and so scribes meticulously copied and preserved it.
Jesus’ appeal to sections in The Psalms indicates that these texts was well-known and therefore points to literate bible readers or hearers who may have used these superscriptions and postscripts in specific or recurring readings.
Source: Titles of Psalms (4)