polar coordinates are "red-haired stepchildren" in Matlab, for sure.
I've not played with the new(ish) PolarAxes, but I think if you simply first create a line handle with the initial point, you can then update the ThetaData, Rdata properties of the line directly. There's an example of a marker following a line at Trace-marker-along-line for a single point; to draw a line you simply add data points to the internal arrays; remember to preallocate an array of NaN for performance instead of dynamically reallocationg by concatenation.
The newer documentation links make the above hard to find; if didn't know it had existed in earlier versions, not sure one would ever find it. I had to do a search for "Animation" to uncover the link. The only thing at the top level I did find took me to the animatedline which we know doesn't work completely universally yet.
NB: EDITORIAL COMMENT/OPINION
TMW gets so enamored with all their new toys they often seem to introduce them before they're fully ripe which is OK if they don't sever the documentation links to the tried-and-true at least until all the bases are covered.
