Interestingly, there was once a full metal jacket .22 Long Rifle cartridge.
In the late 1940s or early 1950s, the U.S. Air Force adopted an over/under survival rifle for use by its pilots. Most of these were .22 Hornet and .410 caliber. Some were .22 Long Rifle and .410.
I don't have my references with me now, so I'm vague on model details.
Anyway, the Air Force issued regular, lead bullet .22 Long Rifle ammo at first.
Then military attorneys pointed out that plain lead bullets in military guns were outlawed by the Hague Convention, for reasons of humane warfare.
To solve the problem, the Air Force turned to ammunition companies. I believe Remington got the contract, though it may have been Winchester.
Anyway, they developed a .22 Long Rifle cartridge with a true copper-jacketed (not plated, as seen on W-W rounds) bullet.
I've seen them for sale by cartridge collectors. They are not a common item and usually fetch $20 to $35 per specimen, depending on the extent of shark feeding going on at the gun show.
I know an old USAF survival instructor, who used the ammo in the 1950s. He said it worked fine and didn't appear to wear out bores any faster than lead bullets. However, they didn't shoot a lot of it, he said. They used the lead bullets to show aircrewmen how to use the survival gun. On occasion, they fired a few jacketed rounds.
The shotgun barrel was another matter. Because it fired multiple lead pellets, aircrewmen were warned that it absolutely could not be used against the enemy.
This always brought a chuckle from the aircrewmen, who figured that if it was all they had, they'd fire the .410 and take their chances with the military lawyers later.
Incidentally, the instructor said that the bolt-action .22 Hornet survival rifle was wonderfully accurate. However, he said the break-open .22 Hornet/.410 shotgun was woefully inaccurate. Most aircremen figured to get close and let the rabbit or bird have it at close range with that, rather than risk a shot with the .22 Hornet and miss.
It was that inaccurate, he said.
I don't know if today's civilian version of the same miltiary survival rifle is as inaccurate today. I've never fired one --- and I damn sure never saw an objective report on one in any gun magazine!
But yeah, they actually used to make a .22 Long Rifle cartridge with an honest-to-god copper jacketed bullet.
Seems to me that such a thing would be popular today, if for no reason but its unusual nature. I should think that Aguila or CCI, who seem to make the widest variety of .22 rimfire ammo today, might be interested in such a beast.
As for using the .22 Long Rifle for defense, I'd carry it as a backup weapon to my .45 or Walther PPK in .380 ACP.
I'd carry high-velocity, standard weight bullets of solid-point construction. This, to me, would be the best compromise between penetration and shock effect.
I distrust the light bullet/high velocity concept, as introduced by the CCI Stinger and copied by others since. From what I've seen, they penetrate poorly. Thick clothing or a wallet in the breast pocket would probably stop them, or slow them down to the point of ineffeffectiveness.