Hey @Nate! Just dropping in with some good news. 
With August’s release, you can now pin both lines and strokes! As you mentioned, this improvement now gives users more control over their template creations using lines.
Thanks again for passing along this feedback. 
You can learn more about the feature in these topics:
Moving and Pinning Pen Strokes and Adding Lines, Line Connectors and Modifying Line Routing.