Numbering monarchs is primarily the activity of historians and people who wrote down what was happening. Both King Edward I and King Edward II, for example, would have been addressed as simply King Edward. Marc Morris' explanation for why Edward I was numbered that way was to clear up confusion over the fact that there were three Edwards in a row covering quite a long period of time. People writing about the reigns of the three Edwards numbered them initially with regards to their order (the first Edward, the second Edward, and the third Edward) but that quickly changed into simply giving them the numerals. This meant there wouldn't really have been any controversy over it during Edward I's life since it didn't become an issue until after his death when the number of Edward's began piling up.

What makes this example so remarkably weird is that Edward I was named after Edward the Confessor so it definitely wasn't out of ignorance of the previous Edwards. Henry III was a very devout follower of the cult of Edward and so gave his son a name that at the time was really quite bizarre. Edward is an Anglo-Saxon name not a Norman name. Morris' example is that at the time it would have been as weird a name as other classic Anglo-Saxon names like Egbert or Egfrith still sound to us today. Henry III's bizarre naming trend continued because he named his next son Edmund, also an Anglo-Saxon name.

While I'm on the subject I always found it interesting how unlikely it was that the three Edwards even happened. Edward II was the last child by Edward I's first wife and the fourth son. Clearly naming his future heir Edward wasn't a top priority for Edward I since he went for John, Henry and Alphonso as names before finally naming a son Edward. This isn't really related to your question, I just think it's interesting.

Marc Morris A Great and Terrible King