'It always strikes me as bizarre and a bit embarrassing to see classicists insisting that it is impossible to acquire fluid or fluent command of Latin or Greek, that "we" can never do this'

I agree with the author. Harder than Latin: musical notation. I don't read it, I "decipher" it. But, lots of people DO just plain read it. Latin is no different than any other language(except for how historically significant it is), it's about dedicating yourself and spending lots and lots of time with it for many years. Saying "we" can never do this is like saying "we English speakers" can never become fluent in Italian, French or Spanish.