Krashen never said that you can learn to speak and write just by listening and reading. He has said that it's a waste of time to speak too early, before you have understood a lot of input. You still have to produce a lot to get better at it. There's also a huge number of studies that show that people who read a lot in their native language speak and write better and studies that show the same effect when learning foreign languages. There's also the practical point that it's useless to be able to speak well if you can't understand the responses you get.
Language is not a one way street. Being able to manipulate another person's actions and words through speech is as much a part of language understanding as being in a position to have others manipulate your actions and words.
Part of knowing a language therefore is being able to speak and write it. In order to learn how to speak and write it, you are not going to get away without speaking and writing it.
And even if Krashen's hypothesis that input is ultimately the whole story were true (which by definition it isn't), production would still play a critical role in memorization. Every time you struggle to find a word and eventually conjure it, it gets reinforced.