If it didn’t include the presidency that would suggest that one could be remain in Congress while being appointed president

No Senator or Representative shall, during the Time for which he was elected, be appointed to any civil Office under the Authority of the United States, which shall have been created, or the Emoluments whereof shall have been increased during such time; and no Person holding any Office under the United States, shall be a Member of either House during his Continuance in Office.

Also I believe the entirely cooked constitution already allows for, e.g. the Chief Justice to be appointed president (subject to some shenanigans around salaries) so why not