How difficult was it for the Roman controlled church of the fourth century on to suppress the alternative gospels e.g. the gospel of the Ebionites?

My research of the study of Christianity shows the Christian canon first formalized at the Council of Rome. This is pretty much 2 years after Christianity was made the official religion of the Roman Empire in 380 with the Edict of Thessalonica. So Rome was already in charge by this time. In earlier works by the Church Fathers there are fragmentary references to a competing narrative today know as the Gospel of the Ebionites . This gospel evidently contained a narrative which was much less objectionable to people of a Jewish origin and faith. No mythical virgin birth. No hint of claiming divinity of the protagonist. Nothing that would support the heretical teachings of the apostate Paul. Clear support for continuing Torah observance including circumcision. Clearly this version was not in line with the Roman agenda which was very much anti Jewish and anti Torah. So just how difficult was it for the Roman Church to suppress these competing narratives? My understanding is that the Ebionites lingered on for several more centuries before being reabsorbed by Jewish communities.