The correct answer is: would.
The word “would” is used to express a possibility or a wish. In this case, the sentence is expressing the possibility that the press would serve the profession better if it were objective in its reporting.
The word “may” is also used to express a possibility, but it is a weaker possibility than “would”. In this case, the sentence could be interpreted as saying that the press might serve the profession better if it were objective in its reporting, but it is not certain.
The word “can” is used to express ability or permission. In this case, the sentence could be interpreted as saying that the press is able to serve the profession better if it were objective in its reporting, but it is not saying that it will do so.
The word “will” is used to express certainty or intention. In this case, the sentence could be interpreted as saying that the press is certain to serve the profession better if it were objective in its reporting, but this is not the meaning that is intended.
Therefore, the correct answer is “would”.