If you're going for staff/principal/senior engineer at Big Tech, this is necessary. (Though I don't think you'll get principal engineer interviews, maybe not even staff unless you have some really notable technical accomplishments other than just being a CTO).
However if you want to work at later stage startups you may not need much practice either.
Finally, you're going for Engineering Manager, I think you shouldn't need to do leetcode. I think most FAANGs etc are going to ask for code reviewing interviews or the like, not have you actually doing algorithmic puzzles.
You do want to practice system design interviews, depending on your skill set, you might be fine and just want to get used to the interviewing process, or you might need to study up quite a bit.