This is the natural way to learn any language. This is the mantra on which the Speak Sanskrit movement was founded in 1981 by Sri Krishna Shastry . You don't need to memorize all the noun and verb tables.
Classes are fun and are conducted through enjoyable games.
The answer is simple - they dont follow the natural way. Speaking and listening a language takes you closer to it. That is the way a child picks up its language. Reading and writing are only the later parts of learning. The extensive research done by Samskrita Bharati on the natural way of learning a language has resulted in Speak Sanskrit Camps.