As far as you go, your original post is correct, but...
Comparison: .1597 / .0989 = 1.61
The .45 ACP frontal area is 61% larger than the 9mm frontal area which is still a significant difference IMO. Note also that typical bullet weights are 115 gr vs 230 gr or 100% heavier bullet for the .45 ACP.
This post is dead (no pun intended) accurate. I have a lot of geometry/physics under my belt, and just because your eye can't determine extra area doesn't mean it isn't there. Look at a 10 gallon fish tank...is a 20 gallon twice as large in all dimensions? Do the math.
A factor you didn't mention is one of Newton's laws of mass. Simply put, a heavier object is harder to stop, regardless of the velocity. Unless a lighter bullet is specifically designed for penetration, it will never come up to the performance of a heavier bullet.
All that being said...I have guns and holsters to carry anything from a .32 ACP to a .357 Mag., to a .45 ACP. I carry a 9mm. Why? It's what I shoot best. Combine that with a relatively high round count and reliable ammo (Corbon 115 gr. DPX), and it works.
As has been said by others, get the idea that any handgun caliber is a reliable man-stopper out of your head, It ain't so.
The caliber war will rage on, and nothing will ever be concluded. People will swear by their caliber. And they should, they depend on it to guard their life.
To each his own...