When we formed Christian Leadership University 25 years ago, we spent a week of training at Notre Dame University with DETC providing the instruction. I have also spoken with professors from numerous universities which have government-recognized accreditation and they all agree that accreditation recognized by the U.S Department of Education requires a lot of paperwork which consumes about 20% of their time each week.
You will need a government-recognized accredited degree for a job which requires government licensing or certification. This would include nurses, doctors, teachers, CPA's, lawyers, state licensed counselors, army chaplain and others.
On the other hand, this accreditation is not normally required for hospital chaplains, Christian counselors who are not state licensed, natural healthcare workers, and people working as pastors, missionaries, evangelists and teachers in Bible schools. In addition, business owners and employees are not required in most cases to have an accredited degree recognized by the Department of Education.
You should ask people who are working in the profession you are pursuing if a government-recognized accredited degree will be required.
Does government accreditation and certification by the state ensure better quality?
I am not aware of any study showing that state certified teachers with government-recognized accredited degrees outperform non-certified teachers. Actually the opposite appears to be true. Homeschooling parents normally have students who outperform public school children in standardized testing. Generally speaking, these homeschooling parents are not state certified, nor do they have government recognized accredited degrees in the area of education. So there is no need to despise a degree that does not have accreditation recognized by the U.S. Department of Education.