It seems hard to conceive of a world where e^ix isn’t important in ML, unless that ML is sans probability, neural networks, or really most anything useful. Perhaps for regressions, so long as they have no periodic component. I think you probably can mechanically, without understanding, skate by in a job without any understanding of trig, but I don’t think you can understand much ML without it, and certainly can’t reason about limitations of an ML technique. While you might not directly use trig, I feel you must use things that were taught using trig to justify the technique and bound it’s applicability.

But really trig isn’t very complex a topic. I don’t think you should attempt to avoid teaching it. I just think it’s like a 1 month topic that is filled in as you learn calculus, linear algebra, and physics. The real intuition of trig comes form the use of it in other areas, and as a standalone subject it’s just boring.