This interesting, I work as a data engineer but never had to really understand how joins or indexes work because I work 99% of the
time with denormalized data. I also do not know much about b-trees. I think you come from the database developer point of you rather than the database user point of view.
There is also other aspect of this, even if I do not understand joins or b-trees I can measure performance so I can figure out which combintion of joins are the faster. The reason that I prefer performance testing over getting to know the theorethical background for certain things is because in many cases your performance also depend on the implementation details, not only on which tree data structure backs your implementation.
It's exactly because the performance depends on the implementation details that when you understand implementation details, it can guide what you test and help find an optimization peak faster - or come up with a theory of another peak more distant, and journey through the performance valley to find it.
Implementation details follow the contours of the fundamental algorithms and data structures. You understand the outline of the implementation details - the bones, if you will - from that. And you can dive into the source (or disassembler - I've done that on Windows) to fine tune knowledge of other specifics, with e.g. gdb stack traces on the database engine when it is abnormally slow to focus attention.
Without having gone to battle together over some performance problems, or me writing significantly longer battle-story posts, we're probably not going to be able to communicate effectively here.
There is also other aspect of this, even if I do not understand joins or b-trees I can measure performance so I can figure out which combintion of joins are the faster. The reason that I prefer performance testing over getting to know the theorethical background for certain things is because in many cases your performance also depend on the implementation details, not only on which tree data structure backs your implementation.