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... Either way you have to use some function of the diameter of the bullet's expansion face to determine the cross-sectional area of the circular face. For this reason, it is the most important factor in play. ...
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You're missing the point. It's not a matter of diameter being important (or not) in terms of calculating cross-sectional area, it's a matter of diameter being insignificant to the larger problem within the range of possible values.
My point regarding diameter specifically is that it doesn't really tell you anything. If the important factor is cross-sectional diameter, why not just not that in the first place? Doing otherwise serves to obfuscate the underlying physics by suggesting that the problem is much simpler than it is. This is one of the giant reasons why things like the Thatcher formula, the Taylor formula ... and whole host of others ... are utter nonsense.
If you want to get into metrology and physics, the very first thing of importance is to make sure you have adequately described the problem in terms of known physical principles, and secondly to be certain you are measuring the right thing. Everytime I see someone use
diameter in some supposed calculation of internal, external or terminal ballistics ... well, I know it's going to be a
gun guy, not a physicist or metrologist.
I'm not going to stoop to the level of insult based upon some reference to a grade level. I'll just note that I do this for a living, and a number of institutions like NASA, IBM and Intel think my work is just fine, thanks.