Details of your operating system and version of Adobe Illustrator
Current version of CC on a Microsoft Surface windows 10 pro

The steps you were taking when you experienced the issues:
It's in both the asset export panel and the export artboard panel. My global preferences are set to inches as well as the originating document.

I'm often creating elements then exporting various bits as assets. So the asset export panel is handy for this. I could just copy and past into a new document and "save as pdf". It's just a smoother flow for my brain to use the asset panel if I can work around this little issue.

But when I have a file with units set to inches and I export an asset or artboard as a pdf, when I reopen the pdf in AI, it defaults to points.

When I open the pdf an AI and go to the Units in the doc preferences it does say inches, but the transform panel is displaying points. If I then switch the preferences to points, save that change, and then reopen the units preferences and switch it back to inches, THEN it displays correctly as inches in the transform panel.

Your expected result:
I expect the pdf to retain the units preference set in the doc the asset was exported from, when opened back up in AI.

Your actual result
Described above. When I reopen in AI, the asset exported from the asset export panel as a pdf, the units display as points in the transform panel even though the preference is set to inches.