But the odd "primus" or "secundus" would certainly come in handy for Murimuth when he has to discuss two Edwards at once; so why not use them? Well, the obvious answer is that the convention didn't exist, as it applied to English kings. Even if it was being used for the Henrys (and I'll have to look into that, because I don't know), that's only one precedent, and one point does not make a line. Since the Conquest, there had only been one Matilda, one Geoffrey, one Richard, one John; though there had been two Williams, they were well in the past, and easily distinguished by descriptors: "the Conqueror" and "Rufus".
So someone writing about Edward I and needing to distinguish him from other Edwards (which was, of course, not a necessity at all until his son became king) could have done so by a descriptor - say, Edward Longshanks - or by a number - Edward the First. The problem was, of course, that he wasn't. His namesake, Edward the Confessor, died months before William became the Conqueror; Edward the Martyr was easily confused with him, having similar mutable stories of sainthood and invasion hovering around his mild-mannered, ineffective and above all brief reign in the late 900s; and Edward the Elder had reigned 899-924.
Marc Morris has this to say on the subject, in the preface to his recent biography of Edward I:
At the time of Edward's accession in 1272, even his most recent royal namesake, Edward the Confessor, had been dead for more than two centuries. Everyone in the thirteenth century remembered the Confessor, for by then he had become the patron saint of the English royal family. But when it came to the other King Edwards, people were altogether more hazy. Towards the end of Edward I's reign, for example, some of his subjects felt compelled to chronicle his remarkable deeds, and decided that they needed to distinguish the king by giving him a number. Unfortunately they miscounted, including in their tallies the Confessor ... and also the celebrated tenth-century king, Edward the Elder (899-924), but overlooking entirely the short and unmemorable reign of Edward the Martyr (975-78). For this reason, at least two thirteenth-century writers referred to Edward I as 'Edward the Third'. Had they counted correctly, they would have called him 'Edward the Fourth'.Murimuth should have read that passage, because he uses neither of those methods to distinguish Edward I. Writing some decades later, he must not have noticed - or perhaps chose to disregard - Edward's contemporary chroniclers who did give him a number, and apparently was not writing late enough for the presence of a third Edward to have solidified the need for ordinals. And so far, he's only referred to Edward I as "son of King Henry" once: not to distinguish him from any other Edwards, but simply on his first introduction, on page 2.
Fortunately for us, such early and inaccurate numbering schemes did not endure. In general, when his contemporaries wished to distinguish Edward, they called him 'King Edward, son of King Henry'. The need for numbers arose only after his death, when he was succeeded by a son, and then a grandson, both of whom bore his illustrious name. By the middle of the fourteenth century, Englishmen found themselves having to differentiate between three consecutive, identially named kings, and so unsurprisingly they started referring to them as the First, Second and Third. Anyone troubled by the recollection that once upon a time there had been other kings called Edward could salve their historical conscience by adding 'since the Conquest'. Thus the Norman Conquest became the official starting point for the numbering of English kings. 
So, how does Murimuth refer to Edward I, after the accession of Edward II? He can't call him "rex Angliae" anymore, or "rex Edwardus". He can't call his son "Edwardus de Carnervan" now that he's king; nor can he call the man who was king "Edwardus de Wyntonia". The solution is to refer to him as Edward II's father, handing the title from one to the other in a sentence in which each is referred to by their familial relationship to the other:
Cui successit Edwardus de Carnervan, filius suus, statim post mortem ejusdem patris sui. (11)
The odd thing about the way Murimuth uses "pater suus", however, is that as Edward II takes over the signifiers "rex Angliae" and "rex Edwardus", "pater suus" becomes so closely associated with Edward I that Murimuth will use it in sentences where Edward II, the target of "suus", never actually appears, where grammatically "suus" could refer to Archbishop Robert, to Boniface VIII, to William Langton, Piers Gaveston, Robert Bruce or any of several people named in the course of a convoluted paragraph. And yet, even in the absence of his son, it retains its meaning: Edward I.
It never becomes quite dissociated from its technical meaning, not quite enough to be called a proper noun in its own right; but it does edge in that direction. And at the same time, the meaning of "Edward I" moves - naturally enough - from the actual king and his historical actions to an exemplar of fatherly almost-perfection against which to judge the actions of "filii sui".
Perhaps I'm reading too much if I see hints of "Pater Noster" there; but that is the main traditional use of "pater" as a proper noun, and makes even common-noun "pater" a very laden word; especially, surely, when used of a king.
 Morris, Marc. A great and terrible king: Edward I and the forging of Britain. London: Hutchinson, 2008. xv-xvi.