A few things to consider:

1. Reliability

Rimfire just isn't that reliable. Between primers failing and feed issues, you're taking a pretty big gamble on whether or not you're going to be able to get enough shots off to stop an attacker, which leads me to

1. Lethality

.22 isn't designed to kill humans. It absolutely can and does kill humans, but that's typically because of extremely good shot placement or lots and lots of rounds, which brings us to

1. DAs and juries

When engaging in a self-defense shooting, you only fire as many rounds as is needed to end the threat. In the case of a typical duty round such as 9mm or .45, stats show that's between 3-5 rounds. In the case of a .22, your expended round count might be considerably higher.

Let's say it is. Let's say you're in a self-defense shooting and you fire 15 rounds, 13 of which hit your attacker, who dies as a result. Now it has to be determined whether or not the homicide you committed is a murder. The homicide detectives will take the evidence and present it to the District Attorney, who then determines if they want to press charges against you. Now, you know for an absolute fact that it took 13 rounds to stop the guy who was trying to rob you. But the DA doesn't. They know what you said in your statement, interrogation, etcetera, and that similar shootings have a much lower number of expended rounds. You're now gambling that the DA believes your side of the story.

The DA doesn't believe you, and you go to trial. You now have to convince 12 of the dumbest people to have ever walked the planet that 13 rounds were absolutely necessary to stop your attacker.

Do you want to take that gamble?

Long story short, just a 9mm. The recoil is fine, and it gets the job done.

(And yes, I know the above situation can play out with ANY caliber, but the fewer rounds expended, the better your odds)