A new thought just came to mind that might shed light on the situation: was it developed in a time and place where the DL was celebrated more often than Sundays (that is during non-fasting periods)?
Partially correct. In the East, presanctified liturgies started in Syria and came to Constantinople during the reign of Heraclius (early 600s). Daily liturgy in parish churches was not the norm in the East outside of Lent during this time (the entire liturgical cycle was stational). However, presanctified liturgy became an integral part of the ramped up Lenten cycle of prayers in all churches. So, in 692, Trullo 52 mandates that "On all days of the holy fast of Lent, except on the Sabbath, the Lord's day and the holy day of the Annunciation, the Liturgy of the Presanctified is to be said."
At that point, Presanctified Liturgy in Constantinople was part of a daily quasi-vigil service. There are several early codices that preserve various forms of the liturgy and of the vigil (the earliest such codex dating to the 700s). The main source for this is J. Mateos, Le typicon de la Grande Eglise
, 2 vols. (Rome, 1962-63).
Also, you'd probably be particularly interested to know that there are many manuscripts that preserve Non-Chalcedonian Presanctified liturgies in Syriac, often (incorrectly) attributed to Severus of Antioch.