So why aren't we all carrying .22s if "shot placement is the key?"
It's a matter of context.
Is there a demonstrable and significant practical difference in the terminal performance of handgun rounds?
The answer depends on the context.
If you look at the entire spectrum of handgun rounds then there is a significant practical difference in the terminal performance.
If you compare handgun rounds
within a general performance category (e.g. pocket pistols, rimfires, service pistol, etc.) then it's much harder to make a definitive statement. Comparing within a general performance category is what we're interested in. No one is in doubt that a .44Mag outperforms a .22LR, but there is a lot of debate when comparing one service pistol round to another.
If there were a definitive answer to that debate then caliber wars would only last as long as it took for someone to find the authoritative quote from the accepted source and use it to prove their point. But there isn't any such quote because it's very difficult to determine the practical difference in terminal performance between service pistol rounds. Experts can't even agree unanimously on what easily measured parameters are most important.
One FBI ammunition expert made an offhand remark in an often-quoted paper he authored stating that the difference in terminal performance as a result of caliber selection (in the context of service pistol calibers) might make a difference in the outcome of a gunfight 1% of the time. Granted, he didn't intend that to be an accurate assessment of the situation but he definitely intended to make the point that it would take examining "thousands or more" shootings to be able to definitively make any reasonable attempt to quantify the benefit.
So what should you do? As long as you pick a gun/ammo caliber commonly thought of as suitable for self-defense that will reliably penetrate to the FBI recommended depth with expanding ammunition and practice/train with it, you won't have gone wrong.
Some might say that's not an answer at all--you still have a choice to make and no way to make it. Well, sometimes when a definitive answer isn't readily available to one question it is beneficial to look at other aspects of the problem and ask other questions. For example, in this case, although it may be difficult to demonstrate a practically significant benefit to picking one caliber over another
in terms of terminal performance, it's easy to demonstrate practically significant benefits to picking one caliber over another in other respects. As we all know, caliber selection can
significantly affect things like concealability, capacity, shootability, practice expense, etc.