He did not need to make the jump to other places. He makes a compelling case that is improbable that life happened by random chance on this planet. He then tries to bolster that argument by pointing to other places where there is no life. I’m not sure what that is called in Latin but it is a logical fallacy.
To make his case he would need to find other places like Earth that are without life.
And, try as we might, we have yet to find other places like Earth...