Do all individuals in H-4 status qualify for an EAD?

No. Only spouses, not children, of H-1B status holders qualify. To qualify, the spouse must hold H-4 status and the H-1B status holder must be the beneficiary of an approved I-140 or have been granted an extension of their H-1B status beyond the sixth year of H-1B eligibility based on a pending employment-based green card application.