Far from me to claim that Harry is competent, but I don't think anything would have helped us in this case. No one wants the job. Everyone has to be bulled into taking this position, so no I don't think that anything would have helped.
That's because you're still talking about procedure, like it's lack of foresight that caused this. Nothing, absolutely nothing would have made it better, because no one wants to be Minister and the ones who might consider it aren't qualified, me included.
I don't think that was the point of the 20 minutes, but it's neither here nor there at this point. I don't think being Draco's friend is a complication, considering they are no longer together.