"cause it to fall over"
A database log file is very different from an OS or application log - despite the common name - it's not an ancillary record of "historic" steps, it's a live running record of ongoing activities with all the data required to make them "done" (committed), or canceling them by rolling back them while keeping full data coherency. It can also be used to roll-forward, replay the actions to restore the state of the database to a given point in time, from a backup which may not contain the latest data. They are more like the "journal" of a journaled file system.
Usually, any change to the database is registered first in the log file, and only later in the data files. And they must be written quickly (that's why log files are often places on faster storage) and committed to disk, so if the instance crashes, the database can be put again in a coherent state reading log data and reapplying or rolling back whatever is needed - often data blocks are kept in memory for performance reasons, and written to disk later. Log files are usually sequential files with a simpler structure that are much faster to write than the much more complex and random access data files.
Remove it, and the database no longer knows where to write those critical data, and to avoid corruption it will usually refuse to perform any activities until a log file is available again. There could be ways to recreate an empty log file, but of course anything not yet applied into the database have been lost - and backing it up *immediately* is needed, because there will be no way to roll forward from the last backup.
There are many reason to protect log files more than data files....