I have similar experience with Spline on Surface. But I found I almost never need them.
Instead I create (or find) a plane close to tangent to the surface. I make my sketch with splines, fillets etc. and use either Split-Line or Project Curve.
Remember "fillets" on a curved surface are not an entity with constant radius anyway, and the splines are more easy to manipulate in the 2D-sketch environment. One disadvantage is that you dont get immediate response when you make changes.