I think your friend might have heard an oversimplified version of the story: it’s possible that many Japanese people can write only a fraction of the kanji they were taught, and that’s definitely what I saw in the kanji street interviews done by That Japanese Man Yuta on YouTube. However, they can still read a good number of them.
It’s true that you can type stuff in rōmaji or hiragana and have it converted into kanji, but in order to choose the right kanji, you need to be able to read and understand them at the very least. Also, almost all written communication contains at least one kanji every five characters, except for children’s books. This is true even in the Japanese Twittersphere.
True in textbooks and children’s books, maybe. Completely untrue in most other cases. Even manga and light novels (which are often, well, ‘light’ reading) contain only unmarked kanji unless the kanji are rare or they represent a name created by the author for the purpose of the story.
Finally, a personal note as a Chinese speaker who was taught probably at least 2500 Simplified Chinese characters in school (the current syllabus probably includes something closer to 2700, but I don’t know the exact number back in my day), and that doesn’t include whatever I learnt on my own later on: I know almost all the kanji I come across, but there were probably about 30 of the most common ones in Japanese that I had to look up once because they were sufficiently different from how they’re written in Simplified Chinese for me to have trouble recognising them. My kanji knowledge isn’t wide enough to read Chinese news without encountering new hanzi though, especially if the article is technical. And even with my kanji knowledge, I still have to learn readings, meanings specific to Japanese, compounds specific to Japanese and so on.
My point is this: I probably know at least 2000 of the most common kanji in written Japanese, and believe me, you need to know them. There really are that many of them that are useful, especially if you’re reading the news, and you’ll see even more kanji in technical writing. The lowest estimates I’ve seen for educated adult kanji knowledge in Japan are around 3000 kanji, and I’d say that my experience so far matches that, because I’m pretty sure there are kanji in technical/university-level Japanese I haven’t seen yet.
However, should you start grammar? Yes, please do start learning basic words, sentences and grammar as soon as possible. It’s good for your proficiency in general, and good for learning kanji, because you’ll eventually be able to learn them in context with understanding. Plus, I think you’ll enjoy yourself more if you start to see that your kanji knowledge is actually useful, so please do look out for things to read after you’ve learnt some of the simplest words and sentence types. There’s no need to wait until you know 2000 kanji to start reading, particularly since honestly, even if you know what a kanji means, you’ll sometimes only have about 70% of the meaning of a new word containing it. (I speak from experience with all the kanji I know.) Learning some kanji/symbols and general language knowledge, applying it, learning some more, applying it, and continuing that way, is probably the best general approach to learning any language. There are definitely ways to be more efficient or to link up your knowledge better, and again, you don’t have to wait until you’ve learnt 2000 kanji to start learning how to use Japanese, but it will take a little while for you to acquire all the kanji you need to read fluently.
EDIT: Oh yeah, I figured I should mention this – you’ll need at least 2000 kanji to read content meant for educated adults with ease, but that doesn’t mean you need to learn all of them on WaniKani, and you may eventually find that you prefer learning through reading/listening/watching Japanese content to using WaniKani in a vacuum. You’re free to learn kanji however you want, and you should pick what works best for you. I just wanted to say that the number we’re talking about (2000) seems quite accurate.