Shouldn't the users on codegolf be able to close their question after let's say the question's winners are announced without them having to have some amount of reputation?
No. The purpose of closing questions is to prevent answers being posted while problems with the question are fixed. If it's a good question, there's no benefit to anyone in preventing everyone from posting answers.
In addition, the last time community feeling on the subject of saying "This person has won: game over" was taken, it was strongly against.