I know how to do this manually, but I need an automatic way (either a script or just a command in Illustrator).
Here’s a line like the one I mean. Notice how it’s all made of straight lines (The blue dots are the anchor points):
How can I turn this into a true curve easily?
Note that I have all of Adobe Creative Cloud at my disposal, so if there is a tool in Fireworks, Photoshop, or anything else that can help, it is still relevant.
You can try
Object > Path > Simplify and adjust the Curve Precision and Angle Threshold settings to perhaps get a curve.
There’s no straightforward method, which I’m aware of, other than this.