but I always wondered why most logging systems employ the rather primitive practice of appending a line to a text file, rather than writing the info to a database
Reliability. Appending is probably the safest way to write to a file. In fact, some file systems have a journaling feature - when enabled, block writes are first appended to an on-disk journal, then are written to their actual destination in the disk. Block write status is tracked in memory and fully written blocks are "shift"-ed off the head of the journal whenever the block at the head is fully written.
Also, having log files being (somewhat) human readable means fewer specialized tools are needed to analyze the logs when something does go very wrong.