The squats and cleans are the test of your core strength. If your core musculature was not strong, you would not be able to do these exercises with any substantial weight. That was the substance of Angel Spassov’s comment that I referred to above and the point Siff emphasized in his books.
This is confusing endurance with strength, which I think is at the heart of a lot of the confusion and controversy over core training. I’m sure you have plenty of strength to execute a sit up. The question is how many can you do? That’s an endurance question.
If you want an exercise that more specifically tests core strength try doing a gymnastics L-sit.
Again, this is a strength versus endurance question.
Within the context of a sprint training program, the high volumes of low intensity core work are not intended to increase core strength except for raw beginners. The specific purpose within regard to the core musculature itself is to increase endurance and work capacity in these muscles in their role as postural muscles. From a general perspective (which is probably more important), the core work is used to develop and maintain general fitness and facilitate recovery along with the tempo running, while distributing the workload over more of the body.