No,
That's another error in logic.
If the .22 is not good enough for the Secret Service to use, that doesn't compel this conclusion. There may be many rounds that work fine.
Example: if the .22 doesn't work, and the Secret Service uses 9mm, you can't conclude that .40 doesn't work.
That is exactly what your logic is. "If .22 was a good defense load, the Secret Service would be using it."
The Secret Service is not using .40, .357 SIG, .45, .380... Per your own statement, if these were good defensive rounds, the Secret Service would be using them. They are not using them, and in fact some agencies have moved away from them, therefore they must not be a good defensive load per your logic and statement.
However, all of that is moot anyway, as civilian use of a firearm for defense is a totally different use than the mission of the Secret Service or any other law enforcement.
The first rule is to have a gun. Most defensive uses of a firearm are successful of stopping the threat without a shot being fired. In those instances, a firearm, any firearm, worked as most folks don't want to get shot. If the aggressor flees at the sight of the firearm, my goal has been met of stopping the threat. I don't need to hold that person or take them into custody like law enforcement would do.
If I have to fire, there are certainly disadvantages of using a .22lr. It is not as powerful as the other cartridges previously listed, nor is the ignition as reliable. However, for a person who may have a disability or issue that restricts their use of a more powerful round, the .22lr can still provide a means of being armed. See rule number one of a gunfight. It is all risk, acceptance of risk, and tradeoff. It may not be the right option for you, but could be one of the better options for others.