Designing 1st person animations is hard, they require more detail, more context, more effects because of how close you are. Similarly, in real life... do you see yourself suddenly in the third person because you do something?
What is so special about the ability being used in the video that it needs to go 3rd person? Other than the fact that it is easier from an art and design perspecitive to just say... yeah make that third person... it requires less detail.
An example of this in the other bungie games would be the pointless 3rd person camera changes in halo 3 when you pick up a larger weapon, or even the chang from first person to 3rd person in the warthog side seat. Only reason they did that is because how imprecise controllers are.
Similarly, you require a less detailed animation set, texture, etc...
To reiterate the above, it is lazy due to less budgeting for appropriate detailed First person art, but also lazy from a design perspective. It is much more complex and stenuous to get something looking right in first person, resorting to third person (when it has nothing to do with FOV problems) is lazy.
Unless it is impossible to communicate what is happening in first person, an FPS game should stay in FPS. It looks more detailed, communicates a sense of presenceand does not break illusion.
Similarly quick FOV changes always look bad. And that is exactly what is happening in this Destiny footage.