[susan53]

Always try and give contemporary examples. languages changes, and if your examples are more than 100 years old, the reason for the difference is just the changes in the language over time. It would make no sense to say eg Shakespeare uses "thou". Why can't I say it now? Find contemporary examples of the language point you want to ask about, otherwise you may just be wasting your time asking the question.

However, here that's not the problem. I think you need to look at the concepts being expressed.

There is no such thing as a countable or uncountable noun. Nouns may be used countably or uncountably, and many can be used both ways. So you are quite right when you say that the concept of "countability" is used to express "a type of". Some examples:

Gorgonzola and Cheddar are my favourite cheeses.
Pinot Grigio is a popular wine from the Veneto region.
She spoke with a sincerity that was moving.


In both these sentences, and your examples of bonhomie, reverence and pulchritude, you could add "type of" before the noun or noun phrase:

Gorgonzola and Cheddar are my favourite type of cheeses.
Pinot Grigio is a popular type of wine from the Veneto region.
She spoke with a type of sincerity that was moving.
There was a type of casual bonhomie between the actors at rehearsals.
I endow her with a type of pulchritude that the women I have seen do not have.
... a type of deep reverence for the poet.


Notice though, that all these examples either refer to concrete objects (cheese, wine, etc) or personal qualities or feelings (sincerity, bonhomie, pulcheritude). Assistance is neither of these, so you need at least to hypothesise that it's the semantic concept that makes the difference
Assistance is the nominalisation of a verb and refers to an action. Nominalisations are sometimes used countably, and sometimes uncountably, and many so-called uncountable nominalisations are used countably in the type of sentence you are asking about. Eg : He has an impressive knowledge of his subject.

but there are a few which only seem to be used uncountably - so if you wanted to add a determiner, it would be some :

She offered me some practical assistance...
We did some careful research into the problem.


That, I'm afraid, is as close as I can get.