The Categories tab is not showing on content elements starting with TYPO3 7.2 (I have not verified if 7.3 has the same problem). I have verified that all content elements in TYPO3 6.2 as well as 7.1 had a categories tab with system categories showing in that tab. As far as I can tell nothing has changed on my end so I believe something changed in the core to break this. The TCA for categories appears to be identical in both 6.2 and 7.2 and well as the install tool default setting of [SYS][defaultCategorizedTables] = pages,tt_content,sys_file_metadata.

Temporary Work Around¶

Boris Schauer tipped me off to manually adding \TYPO3\CMS\Core\Utility\ExtensionManagementUtility::addToAllTCAtypes('tt_content','--div--;Categories,categories',''); to ext_tables.php in my provider extension as a work around, but I didn't have to do this before so I suspect there's a core issue here.