Not exactly.

"It is thought the .45 caliber revolver [meaning the Constabulary Model 1902 ] is the one which should be issued to troops throughout the Army. Instances have repeatedly been reported during the past year where natives have been shot through and through several times with a .38 caliber revolver, and have come on, cutting up the unfortunate individual armed with it. The .45 caliber revolver stops a man in his tracks, usually knocking him down. It is [also] recommended that each company serving in this department be furnished with four 12-gauge Winchester, repeating shotguns. For outpost duty and advance guard [walking point] there is no weapon in our possession equal to the shotgun loaded with buckshot."
-General Leonard Wood, source.

I'm sure I can find other such reports but if I must it'll have to wait until I have time to do so.

"The Luger automatic pistol as a hunting pistol and for dress occasions is attractive and useful. I have one which I prize highly, but for field service, in the hands of officers and men, it is a failure. It is too complicated, and cartridges often jam, but the main defect is that the bullet will not stop a Moro."
-Brigadier General Samuel S. Sumner, commenting on the trial issue of the 9mm Luger in theater during the Philippine Insurrections
(sorry its the same source I've been using, but if I need to find more to satisfy anyone here I will).

I like my 9mm too. It has its uses.
I may be mistaken, but, in California, where you reside, does the LAPD SWAT not still issue a 1911 chambered in .45( I know they used to?), and does the SIS not use a specialized version made just for them of the Glock 30, chambered in .45 auto?

The idea I'm trying to get across here is that yeah, the 9mm will get the job done, but what it can do, bigger and more powerful calibers can do better(even if marginally so). Even with "today's modern ammo".
This (even perhaps marginal) advantage stipulates that the 9mm is not the "equal" of the .45 auto, nor the "better cartridge" overall, and having the advantage of a bigger, harder hitting caliber is still worth it to some folks.

9mm is the perfect balance of power and controllability, but like with all handguns, there are compromises and with the 9mm, the compromises which achieve such mean the round is not going to be as hard hitting(even if marginally) then a round that admittedly recoils more. Its physics. And, there are still benefits in the opinion of others to being able to handle bigger calibers- even if those benefits are marginal and difficult to quantify beyond historical anecdotes and the preference of those who choose them.

And ultimately, its not even really about caliber, its about the person on the trigger, so....... if you can put the bullet where it needs to be is really all that matters.