Why is “的” not necessary when talking about someone's body parts?
In 这个女孩眼睛大,  这个女孩 (this girl) is the subject and 眼睛大 is an adjectival phrase for it. Meaning "[这个眼睛大的][女孩]" (this girl with big eyes)

In 这个女孩的眼睛大,  女孩的眼睛 (this girl's eyes) is the subject and 大 is an adjective for it. Meaning "[这个女孩的眼睛][很大]" (this girl's eyes are big)

Similar example:

[他][眼大] = [he] [is big-eyed]

[他的眼][大] = [his eyes] [are big]

[他][手快] = [he] [is fast-handed]

[他的手][快] = [his hands] [are fast]