The Constitution does in fact allow for lower courts than the supreme Court it is specifically mentioned in article three section one.

"The judicial Power of the United States, shall be vested in one supreme Court, and in such inferior Courts as the Congress may from time to time ordain and establish. The Judges, both of the supreme and inferior Courts, shall hold their Offices during good Behaviour, and shall, at stated Times, receive for their Services, a Compensation, which shall not be diminished during their Continuance in Office."

If there is a problem with the lower courts it is the job of congress to fix not the president to disavow.