Why are CEO's saying they “take full responsibility” for layoffs?

Because it sounds good.

This is the responsible thing to say.

But unlike in scenarios where this phrase means something, such as when your kid ends up in trouble, this CEO is most likely never going to impact the individuals that they "take full responsibility" for again. So the words are quite hollow. Taking full responsibility would mean provide financially for them until they're back on their feet.

Someone explained it in the google lay-off thread.

Rephrasing their explanation:

It’s like a break-up. They are saying “it’s not you, it’s me”.

They employees being fired didn’t do anything wrong and they didn’t underperform.

The CEO says he was the one hiring people the company doesn’t need.

Virtue (Honor, Decency, Ethics) Signalling (Expression, Outward Appearance, Speech)

A charitable interpretation would be them wanting to signal to other employers that the people laid off are still good hires. But I don't know if it's an accurate interpretation.

For the person in charge, saying "I take full responsibility" truly is the correct move when something bad happens. Deflecting the blame universally makes it worse.

We all know someone that always comes up with bullshit excuses. It's never their fault. Do you respect that person?

"Tim Cook... hasn't had layoffs". Yet...

It means that "I am taking full responsibility for this decision. I'm not blaming other execs in the company or the people that are being laid off."