automatic resizing of text frames doesn't work properly with text variables
I have a text frame containing just a single text-variable. The text frame is set to horizontal size adjustment. If the varibale is shorter than the text frame then the frame is resized properly. If the variable is longer the text is being squeezed together. The frame stays as big as it was before.

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Alexxander Shae'en M'taal commented
Glad to see that other people are having the same issue, although this is 2 years old initially, this means I'm not doing something incorrectly, InDesign just hasn't solved the issue
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Jacques Kloppers commented
I've got the same problem. I have an auto-sized (width only) text frame on a master page. Within is a Text Variable (File Name) and it is rendered as an abstract blob of compressed letter shapes on both the master and print page.
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JonHHC commented
I've been looking for a solution to this as well. Using a paragraph style with shading doesn't work either. I find it hard to believe this is an unsurmountable problem for Adobe's programmers.
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Piotr Kocybik commented
I've got the same problem. That's how things are at the rim of Indesign. Unfinished business.