"Why would database software be written such that deleting an ancillary file ( such as a log file of historic steps) cause it to fall over?"
Because the transaction log of an SQL server is anything BUT an "ancillary file".
SQL Server transaction logs are actually split in virtual log files, that are used in rotation. All transactions are written sequentially to it and eventually it goes back to the start / 1st virtual file and starts over, ever-overwriting old transactions.
Other than being where current, non-committed transactions are serialized to allow for rollback or for recovery in case of power loss / unexpected shutdown, it also serves multiple other purposes and that's where "runaway transaction log files" tend to happen to people, but those are actually an indicator of something not configured correctly or something else being broken.
The issue is that those virtual log files can only be reused once they can be cleared; and a few things control how and when they can be cleared.
One thing is ongoing, uncommited transaction. Put simply if you have 10 Gb of uncommited transactions, and 5 Gb of transaction log files... Well, the file will grow. That's normal, otherwise the transaction can't happen.
But SQL Server also has different recovery models (related to how you backup/restore a database).
A "full recovery" database is designed in such a way that by combining (full / differential) backups and transaction log backups, you can do point in time restores down to an exact transaction.
To do that however all transactions must also be backed up! So until a specific virtual file is fully backed up, it can't be freed for reuse. It's typical for fully logged database to have a very fast transaction log backup regime (think 5-15 minutes), because the transaction log must hold all transactions until they're backed up.
If someone sets a database to be fully logged, and then does not get a transaction log backup schedule going, well... They log fill will grow indefinitely, because... well because that's what they asked it to do.
Another reason is replication. The various replication schemes that exist in SQL Server are based off the transaction log: transactions that are commited on the source server, are transferred to the transaction log of target server and then also commited to the datafiles of the target servers. Any virtual log files that contain data that is not yet replicated to even just one of the target server can't be cleared for reuse, so broken replication configurations / failed servers can be a reason for transaction log files bloat.
Oh well I could keep blabbing about that, but yeah confusing transaction log with just "log files" is a classic mistakes that bites every SQL dabbler in the ass eventually :)