It's possible I'm reading too much into this, but there seems to be a lot of body parts which contain the 月 radical:
腿 (tuǐ) = leg
脚 (jiǎo) = foot
腰 (yāo) = waist (also 腰部 (yāobù))
脸 (liǎn) = face
胸 (xiōng) = chest
股 (gǔ) = thigh (also 大腿 (dàtuǐ))
胳膊 (gēbó) = arm
脂肪 (zhīfáng) = body fat
肝脏 (gānzàng) = liver
膀胱 (pángguāng) = bladder
脖子 (bózi) = neck
肚子 (dùzi) = abdomen
脑子 (nǎozi) = brain
腋下 (yèxià) = armpit
膝盖 (xīgài) = knee
肌肉 (jīròu) = muscle
手腕 (shǒuwàn) = wrist
肩膀 (jiānbǎng) = shoulder
屁股 (pìgu) = bottom
皮肤 (pífū) = skin
手肘 (shǒuzhǒu) = elbow
Also: 脉, 胆, 肠, 腑, 脬, 腱. You get the idea; there's lots.
Question: Is there a reason the 月 radical occurs many times in body part names?
There's others that don't have it, e.g., 头 (tóu) = head, 眼睛 (yǎnjing) = eyes, 耳朵 (ěrduo) = ear. Nevertheless, 月 does seem surprisingly common among body parts.