The current summary of a smoothing spline shows the lambda parameter which is hard to connect to the smoothness of the fit when introducing this methodology.
To offer a more interpretable measure of the smoothing spline, the output could add the trace of the projection matrix, aka, the equivalent degrees of freedom (EDF). With the EDF, it would then be simpler to contrast the fit of a smoothing spline to, for example, the fit of a polynomial with an equal number of parameters. The EDF is a component of the output for a smoothing spline in R.