The only part of a phrase which cannot be omitted is ...
... the Head
... the pre-Head
... the post-Head
In this: The farsighted decision not to build near the river has been a great benefit to the community, we have
two noun phrases, both containing a pre-modifying adjective phrase
a pre-modified verb phrase
two noun phrases with post-Heads
an adverb phrase
She quickly opened the letter with trembling fingers contains
a verb phrase with a pre-Head adverb phrase and a post-Head prepositional phrase
a noun phrase with a post-Head prepositional phrase
a post-modified noun phrase
two post-modified noun phrases
He worked just over two hours before giving up contains
a pre-modified prepositional phrase
a pre-modified verb phrase
a post-modified prepositional phrase
a pre-modified preposition
A prepositional phase usually consists of
the Head preposition plus its noun phrase complement
the Head preposition plus an adverb phrase complement
the pre-modifying pre-Head plus the Head preposition
the Head preposition plus a post-Head verb phrase complement
Verbs which never take a noun phrase as the post-Head are
transitive
intransitive
ditransitive
defective
"Unfortunately for me, nobody spoke any English" contains
an adverb phrase with a post-Head prepositional phrase
a noun-phrase pre-Head string 'nobody'
a verb phrase with a pre-Head adverb phrase
a prepositional phrase with a pre-Head modifier
The subject noun phrase in the sentence "The complex reasons for the disaster which have never been properly analysed have been the subject of much heated and uniformed debate in this House." is
The complex reasons for the disaster which have never been properly analysed "
The complex reasons for the disaster
The reasons
the subject of much heated and uniformed debate in this House.
We can't say He is fond because
it's a transitive verb
it's an intransitive adjective phrase
the adjective always takes a post-Head
the noun phrase needs a post-Head adjective
The sentence "She finally acceded to his demands for money is best analysed as
a pronoun Head + a verb phrase with a pre-Head adverbial phrase and 2 post-Head prepositional phrases with noun-phrase complements
a noun-phrase with a post-Head adverb phrase + a verb phrase with a pre-Head adverbial phrase and 2 post-Head prepositional phrases with a noun-phrase complement
a pronoun Head + a verb phrase with a post-Head adverbial phrase and a post-Head prepositional phrase with a noun-phrase complement
a pronoun Head + a verb phrase with a pre-Head adverbial phrase + 2 post-Head noun phrases