Note that this is different from the question Why did the Order bother to guard the Prophecy? The question there was whether the prophecy is worth protecting. I agree that it is not worth protecting.
However, my question is even assuming the prophecy is worth protecting, why place a single guard at the ministry. We know that only those mentioned in the prophecy can touch the recording orb, in other words only Harry and Voldemort can get it.
- If someone else comes, he will not be able to retrieve the prophecy, hence no need to guard it.
- If Voldemort himself comes, with or without additional Death Eaters, a single guard will not be able to stop him, the guard will most likely end up dead, hence no need to have a guard there.
So there seems to be no benefit.
On the other hand, there are several drawbacks:
- Arthur Weasley is almost killed by the snake.
- Sturgis Podmore is captured and convicted to six months in Azkaban. That means one member lost for half a year.
- Dumbledore is unable or unwilling to prevent the conviction. That is bad for morale.
- A lot of manpower is wasted that could be used otherwise.
So why would Dumbledore place a guard at the ministry?
This is already stated in the first two paragraphs, but as this question has been marked as a duplicate, it seems necessary to repeat it: The first sentence already mentions the question that is suggested as a duplicate, and states that this one is different. The other question is about the value of content of the prophecy. This question is about the value of one single guard trying to protect the prophecy.