One more interesting thing: You can kind of see the steering turn limits when you drive with TACC enabled or completely manually.
If you steer around a sharp curve, you can find the moment at which the lane lines go from gray (AP allowed) to black (AP temporarily unavailable). It's definitely related to steering angle at a given speed.
Found a good curve last night, and did some testing:
(speed limit 65):
At 65 mph, manually steering, at the peak curvature AP becomes unavailable, though the lane lines depicted are stable and correctly showing the car's position.
At 65mph, with AP engaged, the car biases very strongly towards the outer edge of the curve.
At 55mph, with AP engaged, car correctly navigates curve without bias.
At 80mph, with AP engaged, car crosses lane line but continues to follow the curve, corrects itself after curve ends.
So, right now, IMO this is purely a software limitation, e.g. a speed-dependent rule of "AP cannot turn the steering wheel more than X degrees". It suggests to me that once Tesla is comfortable enough to raise these limits, we may see all of these curve following problems magically go away.
However, the flipside is, perhaps on challenging roads, slowing down (even below the speed limit) is potentially going to be an AP/FSD behavior. I've driven to Tahoe 50+ times at this point. I can stay in my lane with those mountain curves at 80-90mph if weather is good and traffic permits. AP2 seems like it couldn't negotiate the same curves much above 65mph. That might be a key differentiating feature between AP2 and future iterations of Autopilot hardware.