Stretching the neck is not the same as stretching the vocal cords

Only stretching the neck does not directly effect vocalization, because muscles move the neck. Those neck muscles do not connect to the muscles that are used for vocalizing.
If these muscles connected to each other, your tone would change when you moved your neck, which does not happen.
The larynx is suspended by the stylopharyngeus muscle and the stylohyoid muscle in the air.
The larynx moves freely in the air, and makes the resonance chamber in the front of the cervical spine able to produce good sound.
You actually need to stretch to move the larynx well.
If you extend or massage the muscles around the larynx, these actions can directly impact your voice. Noticeably in time, your vocalization will definitely improve.
Although, only stretching of the neck itself does not relate to vocalization.