Indeed, I agree that you acquire hardly any fluency in classical languages with formal education. I suppose that I don't express this well, but I was trying to say that a natural language formally taught does not readily give you much fluency in it either, whereas immersion would give you fluency more readily and pleasurably.

My analogy would be more like this: learning dead languages in the classroom is to playing arcade flying games like how learning modern language in the sterile classroom is to a flight simulator, and immersion is pilot hours spent.

That is, with respect to acquiring skill in flying, time spent in a simulator is inferior to immersion-dominant learning, even with respect to acquiring skill for the simulator. It is in respect to the accessibility of immersion that I say that there is waste in classroom-dominant modern language learning. With arcade flying there is no such thing as arcade physics in the world, so with respect to acquiring what little skill is realistic, there is no better realistically accessible way.