Binary trees are also something you will never need to know about in 99.9999% of real world programming situations, especially if you're using a sufficiently high-level language. In the real world, there are thousands of other factors, tasks and considerations on your plate other than having to figure out exactly how to manually create a binary tree or even think about it. It's one tiny thing in a sea of issues. Speaking from 25 years of programming experience here, about half that in industry.
Useful? Yes. Necessary? No. And in the real world, you could just look it up, give yourself a refresher, etc. as needed.
I don't generally ask people to implement a binary tree. I ask about what data structure is appropriate to use in certain situations. I.e., do you understand the performance characteristics of basic data structures and enough about how they are implemented to realize why certain tasks are very inefficient if you use the wrong one.
Useful? Yes. Necessary? No. And in the real world, you could just look it up, give yourself a refresher, etc. as needed.