What survives best from Innocent I is his correspondence, and it is the correspondence rather than any single decree that made his reign matter. Writing to Victricius of Rouen, to Exsuperius of Toulouse, to the bishops of Spain and, most fully, to Decentius of Gubbio in 416, he set out a consistent position: that every church of the West traces its foundation to Peter or to men Peter sent, that Roman usage in liturgy and discipline is therefore the norm rather than one custom among several, and that any case of major importance should be referred to Rome before it is settled locally.
The claim was not invented by him. Damasus and Siricius had asserted Roman authority before, and Innocent was working within an argument the see had been developing for decades. What he added was consistency and reach, applying the principle to concrete questions put to him by distant bishops, so that the answers became precedents. The letter to Decentius goes down to details of the sign of peace, confirmation and the anointing of the sick, treating divergence from Roman practice as an irregularity rather than a local tradition.
His pontificate coincided with the collapse of Roman security in Italy. He was at Ravenna as part of an embassy negotiating with the emperor Honorius when Alaric took the city in August 410, and he returned to a Rome that had been sacked for the first time in eight hundred years. The disaster gave force to the argument, made at length elsewhere by Augustine, that the church's authority did not rest on the fortunes of the empire, and it left the bishop of Rome as the most stable institution in a city whose civil order had failed.