IS allows slower shutter speeds but fails to deal with SUBJECT
MOTION...the year-old infant suddenly moving in her crib, or the 5 year
old pulling the dog's ear, for example.

Less noisy high ISO would deal with the subject motion better.

Pair either of the above with a fast maximum aperture (like f/2.8) and
you have the ability to shoot in lower light, capture action better,
but this also brings in the issue of smaller Depth of Field, so your
subject does not stay in focus as well when they move closer/farther
from the camera just after the shutter button is pressed.