I think you’re probably right. Maybe I was oversimplifying, although I did state that there one could argue this position rather than that said position was clearly the case.
There have been periods, such as during the Cistercian ascendancy, when monks were so plentiful that they almost formed a parallel diocesan structure, with many priests being ordained. But personally I would maintain that this was not in keeping with the traditions of monasticism nor the wishes of the founders of the major communities, and that these events represent relative aberrations within an overall time-frame of 1500 years of western monasticism. Monasteries in Europe (and later elsewhere) were intended to foster enclosed prayer rather than evangelise the local populations, but as you say, this was not the focus of all monastics for all of the Church’s history, for better or worse.
People are free to disagree, obviously enough. Best wishes to you.