Music has always had a celebratory function. There are several ways in which composers sought to express a direct link to a person or a place. Think about Dufay’s composition for the cathedral of Florence, Purcell’s odes, or compositions using a theme which spells someone’s name in musical notes (BACH is the most famous example). Since most early music improvisation uses pre-existent material, the ensemble is happy to improvise with a theme which has special meaning to the occasion, thereby personalising the concert.
This is music which will never have been heard before and will never be heard again. A more personal gift could not be thought of (in music).