The favorite saying of trainers at workshops is "It depends" and I'm borrowing that answer from them.
Do we always need a candidate's CV? Does a candidate applying to work with us always need a CV?
It depends.

Recently, a girl wrote to us looking for work in the creative department.
She sent a short, factual email in which she introduced herself and the matter she was writing about, and added two brief sentences about her skills. She wrote, among other things, that she is hardworking and creative and handles writing texts well. A brief correspondence ensued, during which no CV appeared, but it didn't have to – if we had been looking for someone for Anna and Maria's team at that time, we probably would have invited the lady for an interview. With her very first email, she proved that she is hardworking (she did research, found the right person to contact and sent the email directly to her) and likes and knows how to write.
The emails were factual, error-free, written with style and humor. The correspondence was a pleasure,
and a CV at that stage was clearly unnecessary.

But we probably would have asked for a CV at the next stage. A CV, profile link, portfolio, presentation. The form of the document can vary and it's useful, I have no doubt about that, for both sides.

It allows the candidate to gather their experiences and look at them in the context of the position they're applying for. I assume that a CV is prepared individually, because otherwise it makes no sense
(you can really tell when we last saw our own resume ourselves).
For recruiters, a CV is a convenient document for taking notes, writing down questions, quickly reminding themselves of the interviewee and the conversation when there are many of them. Resumes are liked for another reason: the way they are prepared and sent tells readers a lot about the owner.

It's also known that cobblers go without shoes and there are people who don't have a CV because they never needed one, because their brand and personal experiences and recommendations were and still are sufficient.

If you don't have such a brand yet, build it and - in any form, have a resume.