Before the Norman Kings came in 1066 there were a few generations of Saxon Kings, three of which were called Edward but until the Norman's came there was never any convention of assigning a number to their name. The Saxon Kings tended to use epithets instead, such as Edward The Confessor as you have pointed out. The other two Edwards were Edward the Elder and Edward the Martyr.

Edward I was the first Edward of Norman descent and therefore the first Edward to follow the convention of having a number after his name.

Incidentally, Edward I's father, Henry III named him after Edward The Confessor as he was fairly obsessed with him throughout his life.

Might also be worth discussing that Edward I may not have been known as such during his lifetime. He was probably retrospectively known as Edward I after his son Edward II came along and there was a need to differentiate. Consider, for example that even now other Kings that did not have future namesakes still do not have a number assigned to them. That is, we Say King Stephen and King John, not Stephen I and John I.

Please see Why are pre-Norman kings not counted for the purposes of regnal numbers for Kings of England eg; "Edward I" actually being the third Edward who was a King of England It has no answers, but it points to two other questions that have a few answers.

The numbering starts with William as he conquered England and supplanted the Anglo-Saxon and Dane claims to the throne.

Part of that just comes with conquering a people. You've created something new. And there was a lot of Norman snobbery toward the English. As was said above, Edward was named after Edward the Confessor but the Normans thought that was an odd choice to name a prince. They liked Norman names like Robert, Henry, Richard. It only became a popular name in England again because of Edward I. Which shows the general disdain for the native English and need to distance themselves.

However, as early as Henry I there were moves to be more English to connect with the subjects . Henry called his son Aetherling rather than prince. His Norman subjects called he and his wife Godric and Godgifu, the most Anglo-Saxon English names you can get, to mock his Englishness. And Henry III revered Edward the Confessor. So it wasn't just unwillingness to reconcile the Anglo-Saxon kings.

Part of the problem is we'd have no idea where to start numbering. It isn't easy to pin point the first king of England. Alfred the Great is usually the starting point. But he was king of Wessex who never ruled the whole area. He united much of England against the Danes and came to rule Mercia but there were still Danish kingdoms in the north. His son Edward the Elder conquered some of the Danish territory but he didn't rule the whole of England either, really.

So should Edward I be Edward III or Edward IV? Does Edward the Elder count? Not counting Alfred the Great feels wrong.

It's much easier to just restart with William. Where there is a clear if sometimes disputed line.