What are the advantages and disadvantages of binary tree and multi-tree?

binary tree is used for sorting, searching, and so on.
Multi-tree is mainly used for files and databases, because of its small height, it can reduce the number of disk io.
so the question is, since multi-tree is so good, why not replace the application of binary tree? Why do so many places use binary trees instead of multi-forked trees?

MySQL Query : SELECT * FROM `codeshelper`.`v9_news` WHERE status=99 AND catid='6' ORDER BY rand() LIMIT 5
MySQL Error : Disk full (/tmp/#sql-temptable-64f5-1e43d15-44a66.MAI); waiting for someone to free some space... (errno: 28 "No space left on device")
MySQL Errno : 1021
Message : Disk full (/tmp/#sql-temptable-64f5-1e43d15-44a66.MAI); waiting for someone to free some space... (errno: 28 "No space left on device")
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