Why, out of a number of function words, only prepositions are "heads" of phrases?

Question

According to Biber et. al. in the Longman Student Grammar of Spoken and Written English:

For each class of lexical word, there is a major phrase type with an example of that class as the head: noun phrase, verb phrase, adjective phrase, adverb phrase, and prepositional phrase. The head is the principal, obligatory word. In fact, each phrase type can often consist of just one word: the head.

In the previous chapter, the author divides the words, as a grammatical unit, into three major 'families': lexical words, function words and inserts.

As silly as the question is, i'd like to know why do we discuss lexical words, such as nouns/verbs/adjectives/adverbs, as the heads of phrases and out of a number of function words only prepositions serve that role?

I apologize if the question is still unclear and/or inane.

Answer 1

Determiners like "the", "a", and "that" are often considered function words. Further, determiners are sometimes considered the heads of what are called determiner phrases.

Many linguists have abandoned the notion of noun phrases in favor of determiner phrases. For example, classically

the dog

would be regarded as a noun phrase with "dog" as its head. But very many synctacticians now classify it as a determiner phrase with "the" as its head.

See the wiki on determiner phrases or google "DP hypothesis" for more information.

So prepositions might not be the only function words that head phrases.

Answer 2

Function words are in fact considered heads of phrases for many (most?) syntacticians. Complementisers, auxiliary verbs, determiners, tense morphemes, negative particles (in fact particles of many kinds) and more are all heads of phrases. It's more complicated to explain this to learners, so many grammars don't put it that way, and instead have determiners as part of noun phrases and so on. I can't check the Biber et al reference right now so I'm not sure exactly what they say and I don't know what they mean by 'insert', but for a student grammar they almost certainly made this decision (or perhaps it is the theory they subscribe to). As to why prepositions are considered heads even so, it's most likely because as Edwin notes above, they are borderline between functional and lexical items. They are closed class, like functional elements, and many have a purely grammatical function, but many of them do 'have meaning' like lexical elements and so it's easier (for students) to identify them as contributing their category to a phrase.