Recordings are great, and powerful (and I'm very familiar with multitracking - it works for a studio setting, but not so much live ensemble performance which is what I was referring to). But, to someone versed in both sheet music and improvisation, the written form can be freer (leaves more up to you), yet also more precise (knowing the specific harmonies desired rather than whatever happened in the recorded take). It can also be more convenient and efficient for focused practice. You can also take in more visually in a score and see the overall form of something in a glance, whereas with a recording you have to experience it over time and store the model fully in your head.
This is really a "yes and" situation - improvisation and "playing by ear" are great, and have always been part of music (the original "classical" musicians improvised, a tradition we've sadly mostly lost). Improvisation is even more dependent on theory than written music (many folks who "read music" don't actually understand the theory behind it). But being able to read and write is just a super convenient tool, and it addresses use cases that other tools (including recordings) don't.
As with regular writing, it lets you give persistent form and structure to your thoughts. This enables sharing, reviewing, and coordinating in a way categorically different than recordings (books still have value despite the existence of podcasts). This doesn't mean you're "not a musician" if you can't read sheet music, any more than a classical musician who doesn't improvise "isn't a musician" - I'm not trying to gatekeep in any fashion. I'm just saying that both of these dimensions are valuable, and ultimately, complementary.