Doesn’t it depend just on grammar? I think there’s no need to consider their meaning as they should be always without articles. Because they are both uncountable(poverty, affection). Am I right?
I think the use of “a” in those expressions indicates that the characteristic is of a type unique to the individual.
When someone’s work displays “a poverty of imagination”, it generally means a certain type of poverty of imagination peculiar to that person or that work. You may even hear “a certain poverty of imagination”. It’s the same thing with “a great affection”.
Generally, they are uncountable. It’s some specialized understanding of those words so they now became countable. I agree with you. The same thing happens with countable “money” in business.(Could you sum up those monies?)