I agree with your points:
The program was made to instill confidence
Provide an engagement in a sport based on contact
To provide exercise and a competitive nature
It is not combatives,it is sport based contact.
The first phase was not put out to be the Battlefield combatives phase,it was put out to be the first step,the ground work towards the advanced material(no pun on ground work intended) and the sad part is many do not get the other levels.

The second and third phase are more along the lines of previous Combatives training that the Army had.

The Military is incorporating a form of battlefield training as part of the work up phase prior to deployment,in units not provided this training some trained members are developing their own unit training.

As Far as Police:
Ground and BJJ phase should not be a desired intent.