I suspect the wood was air dried, not kiln dried (Was this table custom made in a hobby shop?). I suspect the breadboards were not quite attached, properly, to properly allow for expansion and contraction of the main table boards.
You'll likely continue to have the flexing of the table top, so a crayon filler would likely be your best bet, since the crayon wax would be flexible, also, to some extent.
For a permanent (partial?) repair, which, at this point, still may not "fix" the existing cracks, you'd likely have to saw off the breadboards and reattach them with slots that allow for (better?) wood movement.
Do you understand the concept of a flexible filler and why one may be necessary or most desirable?
Bob's recommendation(s) is/are best.