If it was a real ministry, then what if it acted like a real ministry? On the other hand, the judicial procedures seem so very antiquated, so what if it was a real ministry and stuck in the 1400s, simply because there was no need to change?
First off, the minister advising the prime minister of anything would be courtesy, while he would be really responsible to the crown. Secondly, the aurors anomalous status as both fighters and law officers would be explained.
Of course, then the interesting question regarding Voldie's war would be "What if it was dealt with by the same organizational methods of war that were used in the 1400s?"
Well, for one thing, the muggleborn would be in for a shock...

Fudge was nervous. He sat and fidgeted with his green bowler hat as he waited for his audience with the Crown. For months he had been denying that Vold... You-Know-Who had been back, but now he had seen it with his own eyes, and he had to advise the sovereign that they were in a state of war against a psychopathic rebel, traitor, and oathbreaker.

He had managed to put this off until after Hogwarts sent everyone home for the summer, but then there were no more ways to put it off, and here he sat.

When the footman came and escorted him in to his emergency audience, he was almost glad that the waiting was over. When he came out of the audience, all of that gladness was gone, washed away by stunned horror as he tried to comprehend what was happening.

=oooo=

Bill Weasley was visiting home and talking with his mother when his father came home looking stunned, and carrying a large rolled up broadsheet. When Arthur collapsed into a chair at the kitchen table, Bill went over and asked, "Dad? What's wrong?".

When Arthur let the broadsheet unroll, Bill understood all too well. The large printed words COMMISSION OF ARRAY stood out from the smaller print around it, and Bill let "Oh shit" slip out with out even realizing he had said it.

=0000=

The Drs Granger came home from work at the surgery, to find their daughter standing in the dining room look at a printed sheet with a look of intense puzzlement on her face, as if she could not believe was she was reading, something that they were not all used to. "Hermione? What's the matter?" Hermione jumped, and looked up. "Mummy! Daddy! I didn't hear you come in!"

The two dentists looked at each other, and the Hermione's father said "We just stepped in. What's that you have there?"

Hermione looked at the paper in her hands, and then looked back at her parents. "Daddy, would you know what a commission of array is? This is addressed to me, saying that I am summoned to 40 days of service, by the commissioners for this shire. What on earth does that mean?"

And so on, etc, etc, etc.

Background info – in the 1400s, the feudal system was beginning to break down in england as they needed an army a great deal of the time, and the regular feudal methods of supplying armies could not always keep up with the demand for people, supplies, and money. So they instituted the Commission of Array system, which is sort of like a feudal conscription system. Each area was expected to be able to supply so many men-at-arms, bowmen, horses, supplies, etc, with pay for so-many days at the request of the crown. After the days ran out, the crown had to shell out directly to keep them in the field, but each are had to supply reinforcements as needed. Also, the age to go to war was lower in those times. Add that to the fact that it's wizards, and so physical strength is not really necessary, well, I imagine 15 year olds would be expected to appear, even if only as support.