Hmmmm, are you suggesting stripping discussion of the pentarchy in the lead or are you suggesting different phrasing (if so what do you recommend)?
My understanding is that it was Constantinople's position that Rome objected to (which, granted was at the core of Justinian's pentarchy) but not the idea of the patriarchate system as a whole. Even so, though, it's not like Rome pulled out of future councils or in any other substantial ways severed itself from the emperor at that time. In other words, it is certainly true that there were many violent disagreements, some of which led to temporary schisms, but to my understanding Justinian's system, even if not everybody liked it, became a practical reality (one that indeed helped fuel the fire that pushed Rome further and further away).