By logical, I mean: I can measure the angle between a line and a plane, so why can't I control it?
I ran into that the other day. That would make for a good enhancment request, but while it seems self-evident that there's a single angle between a line and a plane, it's not neccesarily the case.
Ostensibly it seems like everything is there, but if you draw vectors conformal to the plane from the origin of your line, you'll get different included angles at different vectors.
Basically the missing thing in the dimension is the projection normal. when you measure an angle from a plane you're saying to yourself, I want the angle between this line and the vector generated by projecting it onto the plane along the normal of the plane.
The measurement tool makes this assumption and I guess the dimensioning tool doesn't.