A transaction log needs to be cleaned up, which takes time. You might amortize cleanup over many small objects.
> but it does work for eg some file systems---which are also a type of database
No mainstream FS uses the txn log as a primary store. The log(s) are only around for active writes to metadata, as soon as the second write is out the spot in the log can/will be reused. Similar to the clean up case FSes try to batch as many ops as they fit into their log(s) before flushing the transaction.
Apart from the CoW herd (ZFS, btrfs, HAMMER) most FSes either can't or won't journal data by default anyway. -- Which is a fairly often overlooked point, many people seem to assume that a journaling FS means that everything, include their application data, is journaled, which isn't just wrong, but can also be a rather dangerous assumption; depending on application.
A log structure for your database would make the update case more similar to the append case, wouldn't it?
(There are definite limits to that technique, but it does work for eg some file systems---which are also a type of database.)