Explain why. If someone recorded a video with permission then it belongs to them and they should be able to do what they want with it.

No, that's absurd - which is why release forms exist.

In the case of sex videos you might say the video belongs to both parties. Couldn't violations of that be handled under existing contract laws?

You could, but contract law is very cumbersome and difficult to enforce for individuals. You'd have to pay for an expensive lawyer. Moreover, you would only be able to sue for damages, against someone who let's be fair is probably a broke loser, rather than jail time.

A magistrate can even rule that there was an implicit contract that it was not to be shared unless otherwise stated.

Why not clear up this by codifying this?