Structure and usage of the construction - BE of

I have seen various sentences like this:

The availability of two reasonably complete mammalian genomes is of great help to gene finders. – The New York Times

I do my utmost to dress the actors very differently from one another, and this is of great help, both in adding beauty and in facilitating the understanding of the plot. – Encyclopedia Britannica

I looked into this thread and came to know about the meaning of such construction and also came to know that not all nouns are allowed in place of "help" in such construction and mostly in that matter this construction is kind of "an idiom".

In A Comprehensive Grammar of the English Language by Quirk et al on page no 732 Section 10.11 I found some little discussion about this construction:

Some prepositional phrases are semantically similar to adjective or
noun phrases functioning as complement:

That is of no importance.

Furthermore, unlike clear instances of obligatory adjuncts, they can
be used as complementation for copular verbs other than BE, a
characteristic of adjective phrases functioning as subject complement:

That seems of no importance.

Now I tried to change the modifier before "help", like instead of "great" I tried to use "a lot of" but came to know that the following is ungrammatical:

He would be of a lot of help. [INCORRECT]
He would be a lot of help. [CORRECT]

Now my question is why "He is of great help" is correct but not "He is of a lot of help"?