I vehemently disagree. If the government is going to force some sort of religious exercise upon all its soldiers, it had better remain non-sectarian. Sectarian prayers must be reserved for sectarian services. Time and place.
Here is why your vehement disagreement is wrong.
Chaplains are brought onto military service to represent their denominations. The court has found that chaplains are an accomodation of the constitution in that soldiers in a separated environment MUST be able FULLY to practice their religion. They are to be fully qualified, fully compliant representatives of that denomination.
From time to time they are required to be recertified by their denomination. They are one of the few branches of service in which an individual can be removed from service by other than the military authorities.
Therefore, they MUST represent their faith tradition. And if that tradition includes a "Jesus' Name" prayer, then they are representatives of that tradition. You get what you bring on active duty. You cannot require them (by law) to violate their faith traditions.
The proper response of the government is to have NO prayer. It is not to force a NEUTRAL prayer. That would be creating a government-approved prayer and a government-approved religion.
Why doesn't the government just pull some unsuspecting soldier from the crowd and make him deliver a non-sectarian prayer?