If I had a NP such as
Thousands of lives
Millions of people
which noun would be the head noun? I could make a case for each, but I assume there is a correct answer.
For me, this example shows a limitation of the concept of head noun.
@KSHuang asks the intelligent question, which of the following is more "grammatical?"
a) "Lives were lost." b) "Thousands were lost."
Both the examples are perfectly grammatical. The only difference is that as a noun phrase "thousands," playing a pronominal role in "Thousands were lost.", can be thought of as lower status grammatically than the noun "lives."
What is really going on here is that, in the absence of context, more meaning is carried by a) than by b). In terms of meaning, clearly a) is the better approximation to Thousands of lives were lost.
So my answer is first of all to question the usefulness of the term "head noun." However, if you are going to use it, I suggest that you need to assess it on the basis of lexical weight or meaning.
In the noun-clusters as above, " Thousands of lives" / "Millions of people" head nouns are unmistakably 'thousands' and 'millions'.
In its PDF format of shodhganga.inflibnet.ac.in while dealing with English Nominal Phrase in Chapter H(pp40–102) it is said that 'of-genitive'( genitive of measure) post modifies a noun phrase. Later it is stated that numerals in English noun phrase may either be ordinal or cardinal having open-class/ close-class characteristics and function either as determinatives or heads. So numerals can also be nominals.
In English, 'preposition groups' are used as the commonest type of post modifiers having even other nouns in the larger noun cluster.
We may put this to test to ascertain whether it is obligatory or dispensable by considering the post Head string, "of lives"/"of people" as preposition groups.