I've seen it on church calendars in one WRO parish. "Low" masses have been done since the sixth century in the West. I don't really care for the practice, personally, but they were done in Orthodox times. They became more widespread later.
I had read this elsewhere:
The nave belonged to all the people of the city, not just its government. Various groups crearted their own semiprivate spaces there by constructing chapels off the side ailes and by endowing altars. Bologna's duomo had at eight chapels, each supplied with a chaplain. Chapels multipied in cathedrals and larger churches throughout the 1200s. City and commercial corporations built them; wealthy families endowed them as replacements for the older capelle gentilizie in their own houses. This switch marks, perhaps, the older aristrocracy's integration into the new republican regime. Such chapels were tiny churches in themselves, separated from the aisle by an openwork iron or wooden grill, which left them visible to those outside. Inside, patrons found themselves in an intimate space, standing only a few feet from the altar.
Each chaplain was obligated to perform the Office and Mass, and in this age when the quiet Low Mass did not yet exist, he sang them. Sometimes worshippers at one chapel service would have been aware of them music coming from other parts of the building. If the singers tried to match each other in volume, morning in the nave would have presented visitors with a holy dissonance.
a quotation from: "Cities of God: Religion in the Italian Communes 1125-1325 by my friend, Fr. Augustine Thompson
Origins in the sixth century for low mass? That is the first time I have heard this assertion. I am certain that is untrue. The low mass was never made official until after the Council of Trent, circa 1550. The low mass is one of the well known contributing factors to degradation of latin liturgy since the reformation, I know of no positive advantages that it brought the church, only inevitably harm. The minimalist legalistic "low mass" mentality, a mentality that views the liturgy as a "mere obligation to be fulfilled" rather than something matching about in more obvious form the "heavenly liturgy on earth" paved the way for faithful acceptance of the reforms of Vatican II. The "Low mass" mentality paved the way for accepting that the "protestantization of roman catholicism" is a good and holy thing.
The origin of daily mass, now that probably does originate in the sixth century, perhaps thats what you were meaning to say.
Daily Mass is not surprising given the more monastic/celibate context of bishops and post-4th c. latin rite priests (celibacy was required beginning at the end of 4th c.).
I don't think daily mass is an issue, and in the context of a married orthodox latin rite priest, they would not have daily masses anyway due to many reasons. Nearly all the reasons are identical to those of why an orthodox priest using the byzantine rite does not have daily mass.
An exception however, could be during the great forty day fast (Lent) and Advent times, when there is more incentive to have a daily mass.
I do not believe that Low mass is appropriate for any Church, anywhere, except as a rare exception during difficult circumstances, an emergency if such a thing exists. The extent to which they occur is unfortunate and hopefully not going to continue into the future.
It's worth noting that ROCOR appears to have a stronger discouragement against the low mass than the Antiochians, though 90% of the WR Churches in both vicariates do not have them. The ones I am thinking of that have had them are in Colorado, which we might say that is an example of them carring into an Orthodox an unnecessary element of their anglican past. The same churches tend to have many advantageous blessings also however, for example, when they do sing, which they usually do, they sing extraordinarily well !