Not sure what do you mean by computing trees in this context, but I personally as a web dev for 15+ years have never-ever had to e.g balance a binary tree or do any other low level operation of that kind. It's important to learn it at some point to be able to understand how it all works, but afterwords you just don't write the low level stuff yourself, ever. If given enough time I'm pretty sure I could come up with some solution for reversing a linked-list, probably even the optimal one, the same way I could probably also figure out how to fix my car when broken... but that doesn't make me a mechanic
I've never had to balance a tree either. But typically it's because the tree represents something essentially tree-shaped and preserving the structure is important. (For example, what would it mean to balance a DOM tree? Nobody would do that.)
On the other hand, I hope you're not saying that the DOM is the only tree you ever use and in 15 years you've never needed to build your own. If so, consider that companies might be interviewing people for programming jobs that aren't like that.