My understanding: choosing knots for a B-spline can be an arcane task filled with guessing and eye-balling. Penalized B-splines attempt to do away with the choice of knot picking, fitting a spline by:
1) Using many basis B-splines (yes, that sounds oxymoronic since bases over a vector space have the same number of elements -- but the idea is that we consider a linear combination of many B-splines)
2) Penalizing the coefficients of these basis B-splines using some penalty while fitting them to some data set.
Assuming that my understanding above is correct: is there any other point to using penalized B-splines?