There are two different issues here. The first is to do with the way that we talk about and think about inventions. The second are the grammatical features that allow us to use the X in this way.
The Original Poster is quite correct that we use the X to refer to inventions. This is sometimes called the generic use of the definite article. It should really be called the generic use of nouns - with the definite article. In the same way that when we say the elephant we are picking out the genus elephant from the set of all other genuses of animal, when we say the typewriter we are picking out the genus typewriter from all the other genuses of invention.
However, there is a constraint on this use of the with singular nouns to represent inventions:
- The nouns must be SINGULAR, they cannot be uncountable!
Uncountable nouns cannot be used in the generic sense to represent inventions. Compare ...
- The inkwell was invented
- The book was invented
- The Ford Fiesta was invented
- The wheel was invented
- The wig was invented
- the ink was invented * (wrong)
- the lemonade was invented * (wrong)
- the artificial blood was invented * (wrong)
- the fake hair was invented * (wrong)
- the paper was invented * (wrong)
- the artificial intelligence was invented * (wrong)
All of the examples above, because they are represented using uncountable nouns, can only refer to a specific amount, body or sample of lemonade, ink, hair, blood, paper or intelligence. If we want to refer to them as inventions we need to use them without an article:
- ink was invented by ...
- lemonade was invented in ...
- fake hair was invented through
- paper was invented long before
- artificial intelligence was invented by bonobo monkeys working on humans in ...
Notice for example that we cannot say the paper to mean paper the invention, because it is uncountable. However, if we mean a newspaper, then newspapers are countable and this is fine:
- The paper was invented ten years after the printing press.
In short, we can't use The X generically to represent inventions unless X is a countable noun!!
Aside from this very specific enquiry, the Original Poster's concept of when to use definite articles or not is spot on. We use the to tell the listener that they can readily identify the intended thing or person that the speaker is talking about. Otherwise we use a with countable nouns or zero article with plural and uncountable nouns. This indicates to the listener that they don't know which specific thing or entity the person is talking about. However, conventions for buildings, places, names, animals, inventions, diseases and so forth are very complicated. They're best studied and analysed individually - in my experience.