They could have "constructively" been found on the menacing charge, but police almost always over-charge defendants and prosecutors try to make the charge stick, when they know better.
The problems arise when the defense lawyers, who consider themselves more 'officer of the court' than defense lawyer, and they allow the lesser included charges to be found for at trial. If you don't know the law, as a defendant, you can and usually are hamstrung by the bastard you are paying to guide your defense.
Religion is regarded by the common people as true, by the wise as false, and by the rulers as useful. Lucius Annaeus Seneca
“One believes things because one has been conditioned to believe them.” – Aldous Huxley