Records had to be batched into blocks and blocks had to be organized for fast access on a spinning drum or platter. This is why we have B+ trees for databases

Records had to be batched into blocks and blocks had to be organized for fast access on a spinning drum or platter. This is why we have B+ trees for databases, and not simple binary trees or whatnot. You need the branching factor in order to reduce the seek times: each tree node traversal goes to a different block of records. If they are on the same track, it takes rotational latency to get to the block. If they are on a different track, seek time plus rotational latency. Reducing rotational latency is why we got 7200 RPM and faster drives: going from 3600 to 7200 means any block is available twice as often at the drive head. It doesn't matter how many or how few have been crammed onto the track; density doesn't fix latency.