I suspect this is a frequency thing. Early SpaceX broadcasts were pretty rough. NASA just doesn't do launch coverage with the same sort of cadence.
Honestly, they should consider outsourcing that bit.
Was going to say, I think everyone forgot about early SpaceX product quality.
And NASA probably does have great video of it available, it’s just the live broadcast that missed it.
I think this is a “you have one job” kind of thing for shooting liftoff (no matter what quality of equipment is on hand): rocket goes up, tilt camera up.
Bonus: Try to match the speed of the tilt with the speed of the rocket in the frame.