There can be a number of situations where one can not get to the back side of an outer race, or where the race design will not allow you to get good contact with a punch.
I just ran into this on a 1926 Chevrolet front inner wheel bearing.
The trick I learned years ago, which I used here, was to run a bead of weld around the surface of the bearing race.
As the weld cools it contracts, pulling the diameter of the race in with it.
In most cases the race will almost fall out after the weld has cooled.