I think there is a lot of overthink here.
The real answer is no one knows exactly how the arrows evolved.
However, it is reasonable to assume it would rapidly become obvious what worked well for different purposes. They wouldn't have "measured" FOC*, but they would soon learn what went through mail, what was best against plate, what worked for hunting and what was most lethal against a unprotected animal or man.
I'm sure some arrowsmith would make a stupidly heavy head just for fun a joke and thus they would find out what worked and what didn't.
It doesn't need calculation, CAD or any fancy measurement, just a bit of trial and error and some common sense.
They would doubtless compete to see who could shoot the furthest and who could smash through the thicker boards.
In terms of military arrow heads they would be made in vast numbers and the usual constraints of speed of manufacture, use of material and suitability for purpose would soon result in a rough standardisation. I daresay if you produce a barrel load of arrow heads to the tower of London that were unsatisfactory you would receive a rather curt E-mail
Del
* I daresay people balanced arrows on their fingers but they wouldn't have put numbers to it... maybe they preferred one that balanced near the point for some uses and one than didn't maybe for flight shooting.... we'll never know.