Literacy rates are tanking as a result; Mississippi went from 49th to 1st in literacy by ditching the new-fangled whole word contextual style and going hard into phonics. Get them hooked on phonics again, then teach them Greek & Latin! Spanish/French/German/whatever should be the *second* foreign language they learn, gated behind Greek & Latin being their first. It was a huge disservice to my education that the 'dead' languages were not offered to me in [junior] high school. I can only conclude that the curriculum and test writers only want literate-enough workers who can't critically think but who can [barely] read and follow written instruction.
Note also that Greek words used in English are almost exclusively scholarly words (like "metaphor", "diagnosis", "theology"), they are not popular borrowings like many Latin words ("difficult", "pork", "to count").
Ancient Greek is a very difficult language. It takes a solid decade of work to learn, and the payoff is you get to read a few - admittedly brilliant - authors. I would not automatically prefer that to being able to talk to everyone in the Spanish-speaking world - or to learning la belle langue. Also, I don't think Greek was ever learnt by the majority of pupils.
My high school was more classical than most and it was not a better way to teach English.
Right after I graduated the one Latin teacher they had retired and that was it.
This exact failure in 1960 California replacing phonics with whole word recognition led to backlash, including one teacher, Barbara Baker, who in 1963 formed Challenger Schools to emphasize phonics, academics starting in kindergarten, curiosity, and beyond minimum standards achievement/excellence.