I think the reason for the "Mexican Magnum" moniker was that before the present day total ban on privately owned firearms the government had a restriction of firearms of any caliber used by the military or police. Therefore 38 Special, 9MM Parabelum and 45 ACP were off limits for civilians. The civilians and private security fell back on 38 Super in a 1911 format delivery system. I do know that's still today they are easy to sell as tortillas along the border.
Not just Mexico. The model for this law is also used in numerous countries. Italy comes to mind immediately. It's one reason that some gun mfgs. continue to make semi autos in 30 Luger.
I've always heard that 38 Super was a good self defense caliber. The ft/lbs. of energy at the muzzle is higher than that of standard ball 9mm and 45acp (about 350 ft/lbs.), which are about the same.
I have a lot of 45acp guns because I like it, not because I percieve it as a wonder caliber

I also like that thick cross sectional density of the big cartridge. Like many, I just don't want to start stocking another caliber. Same reason I keep my 9mms over 40 S&W (I have only 1, a full sized HK USP). I think they are both abundantly lethal in practiced hands.
I try to remember with modern calibers, that the energy delivered on target at close range is completely focused on a spot about a half an inch square and smaller, not spread out. Even 200 ft/lbs. of energy (38 Special or .380) focused on soft tissue and bone at close range has a lot more power than we give it credit for. That's really a lot of damage for mammalian tissue to suffer. I think shot placement is paramount.
The numbers become somewhat abstract to me when reading ballistics figures unless I think of performance in those terms.