Is English article system flawed?

Say I want to use a noun associated with two dimensions: Quantification and Specificity. I find it hard to use a noun to not tell the quantity and specificity of the noun.
Allow me to use the example below to illustrate my concern, and meantime I will try to prove that the English article system is flawed.
"We should use____hammer(s)" Fill one of the articles(a/an/the) in the blank.
List of situations:
Q+ (Quantity positive) means that the speaker knows the quantity of the noun and want to acknowledge the listener.
Q- (Quantity negative) means the speaker does not know the quantity of the noun or does not want to acknowledge the listener.
S+(Specificity positive) means the speaker is pointing at specific individual or subset of the whole hammer class.
S- (Specificity negative) means the speaker is talking about the general sense of the noun.
1. Q+ and S+
Answer: the hammer/the hammers
2. Q+ and S-
Answer: a hammer/ (some) hammers
3. Q- and S+
Answer: the hammer (Arguably, the best I can think of)
4. Q- and S-
Answer:the hammer (theoretically best answer is the singular form "hammer" without any article, but incorrect in English grammar, which is the reason I think the English article system is flawed and dull. The English grammar forces you to use articles preceding the countable nouns.
I found out that "the hammer" form can cover 3 situations. The word "the" is so ambiguous for me, which makes me frustrated sometimes. The combination of article and numeral form of the noun(Singular and Plural) is supposed to convey the specificity and quantity of the noun. But I want to ask here that what happen to when the speaker doesn't know neither quantity nor specificity of the noun or doesn't want to acknowledge the speak even though they know it. If we use "the + noun" form in this situation. This form can cover 3 situations. Here comes the question, what exactly the word "the" means in these 3 situations. People may say that you can tell the difference according to a more detail fledged context. But really? Tough a hammer sits right in front of the speaker and the listener, the listener still can't tell whether the speaker is telling the general sense of hammer or that particular hammer sitting in front of them. For example in Chinese, in example 4. We simply can say "We should use hammer", which can avoid the conflict with "the hammer" in specific context. I want to say the English article system with only a/an/the is very much flawed.
I saw there is tons of work about English articles online. but all failed to come out an explanation to cover all the usages. I think it is because that the English article system is flawed just like the 'American justice system' or any other things created by mankind. I personally think most of linguits failed to see it. I think this is the reason why linguists can't come out better explanation for articles.