"Reading is the key to good writing" and "a large amount of reading results in a good writer" are two completely unrelated.
Reading is considered key because of exposure; reading books across different genres exposes you to many different ways to express an idea or thought using the English language. However, without practice, a person who has never written in his or her life will never become good at writing because of a lack of experience. Reading builds the lingual base you need, and practice builds the experience base you need.
I don't think that reading a lot results in the overuse of cliches; lazy writing does. Writers don't come up with ideas out of nowhere (though some do write by the seat of their pants), and writing is nothing like making a collage; you are not cutting out characters or scenes from different works and slapping them together; you are taking a core idea that the plot is based around, whether that be a character or synopsis, and building on it. That is not a cliche. A cliche is just an idea overused to the point where it characters, scenes, and even plots can be predicted in advance. Good writers do their best to recognize and avoid cliches.
As for whether or not VNs, light novels, films, or other works of expression can help a person improve his or her writing, of course they can. But this is heavily dependent on quality; if memory serves me well, translated works have a rep for have sub-par writing in the form of adjective and adverb abuse, as well as unnecessary filler and a lack of effort to change from passive to active voice.
Films are a bit different; while visual media does not help you with reading, it does contain a lot of dialogue, and that can expose you to verbal cues and tics.
I do agree with your friend when it comes to books and imagery; A book uses only words to present a story. Light Novels and Visual Novels both use CG, with the former also having music, while films have actors to play the characters and don't need to be read. Only in a book will you, the reader, be forced to create a mental image of the characters, the scenes, and even the worlds by yourself, which none of the other mediums do.