While important, the whole episode with Andromeda has really been a sidequest. Perseus still hasn’t saved his mom from Polydectes. And, wouldn’t you know it, they don’t believe that a guy like Perseus could have possibly slain Medusa and taken her head. Therefore, “greeted by a storm of insults [Perseus] displayed the Gorgon’s head, averting his own gaze as he did so, and turned them all to stone.” Yeah, he went nuclear on them. It’s getting increasingly easier for Perseus to take the nuclear option.
It’s surprising, then, that Perseus hands Medusa’s head over to Athena, as simple as that. There is no prolonged discussion, no need to convince him. It’s as if Perseus knows that this is the way to do things. He’s retiring from the hero biz. He also gives up his sandals, wallet, and helmet to Hermes. And while the adventuring gear might be understandable, Medusa’s head is a strategic weapon that would be useful to a king.
He’s already proven its usefulness in dealing with a large number of enemies. No army, no matter how great, would be able to stand against Medusa’s head. He would be able to ensure the safety of his people for as long as he reigned. And that’s the problem.
First, there’s no guarantee it would only be defensive. Yes, he’s acted responsibly so far, but power corrupts yadda yadda. He showed restraint with the Kraken and with the attack at his wedding, but had no problem petrifying Polydectes’s entire inner circle. How long until Perseus went from a great defender to a monstrous conqueror?
Problem two is much scarier. Let’s say that Perseus continues being Perseus and does the right thing for his entire life. He’s still mortal. He’s going to die. Then what? The Greeks don’t exactly have a great track record when it comes to succession of power. More than that, who is to say that Perseus’s heir, or his heir’s heir doesn’t become a bloodthirsty conqueror? Medusa’s head is far too powerful a weapon to leave in the hands of someone who will not use it responsibly?
Also, such a powerful weapon makes him a target. While no one will want to send entire armies to become petrified, every neighboring king will resent Perseus having such a weapon at his disposal, and they’ll want it for themselves.
The wise solution is exactly what Perseus did, turn it over to Athena. This kind of wisdom is not seen in many of the Greek heroes. Odysseus, Achilles, Agamemnon, and Jason certainly didn’t show this much wisdom, either. But we’ll deal with those another time. Perseus willingly surrenders these powerful weapons, and also demonstrates that he will be a wise king. He goes on to further the entire Perseid dynasty, which is mostly peaceful. He and Andromeda are also immortalized as constellations. Andromeda’s parents are there, too, but theirs is a punishment.