Under what legal theory is intending to do something which is legal (hiring a person that has a voice you want) becomes illegal because there is another person who has a similar voice?

It's not intending to do something legal, it's intending to do something illegal: Stealing their likeness. The fact you used an otherwise legal procedure to do the illegal activity doesn't make it less illegal.

How can something be illegal if every step towards the objective is legal? This would result in an incoherent legal system where selective prosecution/corruption is trivial.

It is legal to buy a gun, and legal to fire a gun, and it can even be legal to fire a gun at someone who is threatening to kill you in the moment, but if you fire a gun at someone with the intention of killing someone that happens to be very, very illegal.

Very well. But in this case the end goal is the end of someone's unique life.

In the case of acquiring a likeness, if it's done legally you acquire someone else's likeness that happens to be shared with your target.

The likeness is shared and non-unique.

If you objective is to take someone's life, there is no other pathway to the objective but their life. With likeness that isn't the case.

So? You're merely (correctly) pointing out that the acts have consequences that are of wildly differing severity. Not that one is a legal and the other is not.

OpenAI should hire you as their lawyer.

What's illegal, in general, is not the action itself but the intent to do an action and the steps taken in furtherance of that intent.

Hiring someone with a voice you want isn't illegal; hiring someone with a voice you want because it is similar to a voice that someone expressly denied you permission to use is illegal.

Actually, it's so foundational to the common law legal system that there's a specialized Latin term to represent the concept: mens rea (literally 'guilty mind').