You don't have to change to F-1 so as to attend school - 回複：連我都知

Being in F-1, you can work as RA/TA legally and can apply CPT/OPT, which are not granted to non-F1 international students. Yes, you can attend school in H-4 too.

However, you may apply an EAD after submitting I-485, which entitles you to work as RA/TA and afterwards.