Is there a reason the 月 radical occurs many times in body part names?
Similar questions have been asked in both Chinese and Japanese StackExchange before. In summary, what appears as 月 in printed text is actually the graphical merger between ⺼ (simplified form of 肉 (meat; flesh)) and 月 (moon). Traditionally, you wouldn't handwrite characters with the ⺼ radical with two horizontal lines as the inner two strokes; they would be diagonal.

The similarity in appearance is normally not a source of confusion, as the vast majority of characters which contain a ⺼ component does not have ⺼ appearing on the right, and the vast majority of characters which have a proper 月 component appears on the right, with some rare exceptions (see this).

As a final note, if you wish to understand why characters are written a certain way, looking at the Simplified Chinese form is generally not helpful. 头 has undergone a very contrived simplification from the traditional 頭 (see this excellent answer on Zhihu), and like 頭, characters to do with 'head' may be written with the 頁 component instead of ⺼ (e.g. 頸, neck).