"1. The company cannot hire you under H4 EAD;
2. The program (H4 EAD) will soon be discontinued and
3. You will not be able to move back on H1B visa status."
Let us analyze the three arguments. First it should be illegal for an employer to say they cannot hire on H4 EAD because the EAD is a work permit. Most states does not allow such discriminations. Second, so far the H4 EAD is strong and nobody has been able to discontinue the program. Of course, there is a possibility it might be revoked but so does other executive programs. Third, once someone is cap exempt and continue to qualify as cap exempt, that person can always move back on the H1B.
Based on the above, we recommend that if you have a chance to move to an H4 EAD, do not be discouraged just because the employer is discouraging you. We recommend you speak to an experience H4 and H4 EAD attorney before you make a move. Feel free to contact us at 510 742 5887 for any questions.