The problem arises when EO's are issued pursuant to no particular law, but rather the mere wishes of the president to have his way. That is where Obama routinely crossed the line. His "phone and pen" crap reveals his contempt for legislative due process. An EO is not an alternative to a new law.
The implied powers doctrine has taken this idea way too far so that now we have an unconstitutional fourth branch of government accountable to no one called the Administrative State or Regulatory State that issues unconstitutional "regulations" which are laws not passed by Congress.
Often if and when Congress passes a vague law, the President should before signing, send it back asking for more specificity.