Where I saw the inserts were on ranges where they were using .22 in 7.62 for training.
I was told the lower recoil made it easier for new shooters to get used to the rifles and that it made it easier for the instructors to correct things like flinching.

I thought they were really just trying to save the ammo cost. That counts for a lot in my opinion.
.22 long rifle is about 5 dollars for a box of 50 and my 30-06 costs about 50 dollars for a box of 20 shells.
A day at the range can easily see a brick (500 rds) of .22 gone.

Also by using the .22 instead of the 7.62 they were able to set their range up inside an auditorium so they were able to practice even when the weather was bad.

I didn't think much of the inserts for accuracy. If you were doing it for survival you might be better just getting a light .22 rifle.