Maybe during the Arian period there was some doubt as to the quality of teaching of BoD,

What do you mean "some doubt"? It was not taught by ANYONE prior to the time of the early scholastics except one idle speculation of St. Augustine. Now, St. Augustine later retracted the opinion forcefully and has some of the strongest anti-BoD statements on record, but the early scholastics did not have access to his entire body of work and were not aware of the retraction. But the early scholastics found themselves in such awe of St. Augustine that they accepted too much of his speculations as theological fact. When Hugh of St. Victor and Abelard were disputing over BoD, Peter Lombard went to St. Bernard to help settle the controversy. St. Bernard simply responded that he'd rather be wrong with Augustine than right based on his own opinion ... thereby admitting that it's possible St. Augustine got this wrong, but just yielding in humility. So Peter Lombard wrote the earliest scholastic-type manual. From there St. Thomas Aquinas picked it up ... and then it went viral through him. THAT is the true history of BoD.