I'm going to take a guess that your agitator has an auger at the top,
and while the lower part is moving fine, the auger isn't ratcheting as
it should, giving the impression that the whole thing isn't agitating
as vigorously as it should. Most Kenmore washers come with a parts
list so that you can see a parts breakdown of the area. If the auger
isn't ratcheting, then replace the agitator dogs and you will be up
and running just fine.