Why is disk I/O the thing index structures are actually optimizing for?
Reading from disk (or even from a cold page cache) costs orders of magnitude more time than an in-memory comparison. An index structure's real job is minimizing the number of disk page reads needed to find a value, not minimizing the number of comparisons — which is why B-trees are shaped around fitting many keys per disk page, not around minimizing tree depth for its own sake.
Answered in
What Actually Happens Inside a Database Index: The Data StructuresAn index trades disk I/O for lookup speed. Here's how B-trees, hash tables, and bitmap indexes each make that trade differently.
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