Extend Sensitivity Labels propagation to content authored in Power BI Desktop via live connection

After enabling sensitivity labels on a dataset in Power BI Service all new content authored in the Service based on the dataset inherits the labels.
Content authored in Power BI Desktop (which is the preferred and recommended way) via live connection to those same datasets currently does not inherit the labels even after being published to PowerBI.com

This seems like an oversight and is very hard to govern and document, especially in the scenarios with centralized datasets residing in designated data workspaces.