I can't believe InDesign doesn't have a feature that allows for the reuse of snippets of text in multiple documents, but I'm afraid I'm getting nowhere with the various proposed solutions to this problem.
I appreciate everyone's input, but nothing appears to work as expected or desired. Rather than waste more time on this, I'll just stick to the old cut and paste method.
Hi Owen,
yes. Currently that's the best you can do for now.
The 2 rules with Linked Text (the feature, not the workflow) are as following:
1. Whole stories only.
You cannot link on e.g. paragraph level or below.
2. No anchoring of text frames with Liked Text.
Just plain text frames.
A chance perhaps:
Rule 2 can be overcome with links to files like *.txt, *.rtf, *.doc or *.docx.
Solution:
You could try to export to Tagged Text. And import of files with Tagged Text. Updating changed files would be possible. Relinking to other tagged text files would be possible. Also when working with anchored text frames.
How will that work?
Select all text of a story and export that text to:
Adobe-InDesign-Tagged-Text
Export options:
Tag: Ausführlich // Sorry for my German UI, "Ausführlich" could be translated to "lengthy" or "verbose" perhaps.
Kodierung: Unicode // Encoding: Unicode

That will create a "special" txt file that should not be edited with a text editor if you never worked with Tagged Text or tested a lot.
That txt file can be placed and linked with other InDesign documents. Formatting could be maintained, if the recieving document does not have the styles used in the source document. Not tested, but I think that formatting will adapt to existing styles of the target document if the styles exist prior placing the tagged text file. ( But test that yourself, I did not investigate that very much. )
For that place and link workflow you have to change the placing options of text files in the InDesign Preferences so that links are created. Updating contents and formatting would be possible in a semi-automated way. You will be notified if the links are outdated. Or you could select the text in the target and place again a different tagged text file to update contents and formatting.
I just tested this with a simple story where I formatted text using a custom paragraph style and a character style. For best results be very strict with formatting, test very carefully. The devil's in the detail, I guess…
Regards,
Uwe