I generally leave my splines unconstrained. I only constrain those points/tangencies that require constraints. Because my splines are typically in different sketches, or if they are they are not constrained to each other. This way modifications to one spline don't effect the others.
There are just too many constraints to apply to splines to do it any other way. I have used the "fix" constraint when I want to adjust multiple splines in the same sketch.
I tend to leave my splines unconstrained except for specific relations that are necessary. If you're working with a particularly long spline or a sketch that has multiple splines, fully defining the splines will add a lot of time to your rebuilds.
I think you have it right on the mark with "it depends on the application". I get pretty frustrated with splines so when I get them where I want them I fix the points. Once in a while I will generate a DT to dimension a spline if I am using a conic that needs to be controlled using a Rho value and it will be edited frequently. I try to avoid splines as the surfaces generated using them are not as accurate as those generated using the sketch tools available in the menus.