Yes, but the generated shapes are based on the curve primitives used. The whole point of this particular curve primitive is that the “default” shape of the spline (if you don’t try to set the tangents explicitly) doesn’t extend much past the knots, because of the half-turn periodicity. As you drag a knot away from the spline, you will get a cusp shape with the knot at the cusp, and if you drag further it will turn into a loop with the knot at the peak of the loop.

If you instead had a full-turn periodicity, you would have substantially different properties for the curve shape. Several such curve primitives exist, you can use one of those if you want. This is one of the trade-offs involved in the choice of tool.

With this particular type of curve primitive, the primary way to change the spline is by adding and moving control points, not by trying to manually specify tangents. The latter should not be used for general shape design but should be seen as a specialty tool to support niche technical requirements (such as straight segment to curve interfaces), and tangent adjustments should be sparing because large tangent adjustments will create lumpy shapes.

Sorry I dont share your idea of correctness between this control parameter and its formulaic effect. We might say the formula naturally wraps this angle, but the formula doesn't mind what space we prefer to map from.

> If you instead had a full-turn periodicity, you would have substantially different properties for the curve shape

We would have precisely the same effect on curve shape from a 360 degree control than with a wrapped 180 degree control, but have twice as much travel to adjust the outcome more finely.