Good day,
Why this function is not documented?
There are hundreds of elements in SQL servers that are not documented, just like in any large complex application. Some of the elements are intended for internal use of the application and some are intended for use by the team developing the application or by the team supporting the application.
There are many elements that are not confidential but Microsoft does not want to take responsibility for them because they are not intended for normal user use. In such cases, for example, the Microsoft team usually happy to share the knowledge unofficial in their blogs, but not officially published in the documentation. Official documentation makes the element part of the official product and restrictions and duties apply accordingly.
Paul Randal for example used to write a lot about the internals of SQL Server and undocumented features while working at Microsoft developing the SQL Server. Today he is not longer at Microsoft but still, I HIGHLY RECOMMEND to follow his blog and read his posts about the server internals. By the way, he also posted about this function.
Using it makes we lost product support?
(1) You can always prefer to backup the database log file and use fn_dump_dblog which give the information from backup file. This way you sure that you do not touch the production.
(2) (For the sake of the responsibility and the forum let me add "as much as I know" and remind you that anything that you do with undocumented feature is by definition not supported!
So, as much as I know... fn_dblog is a read only function, which mean it does not change anything.
It can be documented on official documentation?
It can if Microsoft will want to do it and they probably do not for the same reason that I mentioned above.
You can open a request in the UserVoice but I have a feeling that this will not be accepted: https://feedback.azure.com/forums/908035-sql-server
I hope that this cover the questions :-)