The New Liturgical Movement had a recent post about apse mosaics commissioned by Pope St Pascal I (817-24) for three churches he rebuilt in Rome, and linked their design to that of an earlier church rebuilt by Pope St Felix III in 527. This choice by Pope Pascal was in turn interpreted as a clear Roman response to the Iconoclast movement in the East.
It also suggests to my mind that there was a sense of what was right and proper for a Roman church, indeed a very Roman sense of standing in and showing fidelity to a tradition. That can apply to liturgy, to art and architecture and to the enunciation of Papal claims as to the governance of the Church.
The illustrated article can be seen at The Roman Mosaics of Pope St Paschal I
It occurred to me that not only were there stylistic similarities expressive of a recognised tradition in much later Papal commissions for Roman churches from Pope Nicholas iII (1277-80) and from Pope Nicholas IV (1288-92) but that these also have been viewed as having wider importance. George Holmes in Rome Florence and the Origins of the Renaissance sees them as inspired by rediscovered Classical paintings and thus amongst the very earliest of Italian Renaissance works. This book by Prof Holmes, who I had the privilege of knowing slightly in my early years in Oxford, is one I would recommend as one that places later cultural developments firmly on medieval foundations.