I think the reason why the 'naming of parts' approach to 'grammar' hinders an interest in grammar and language is that it presents a false picture of how grammar works.
I believe that humans invented grammar as a branch of human behaviour. If we are to name parts of grammar it is a mistake to treat grammar as if it is a sealed system on the 'communications' model.
'Determiner' is a classic case of this type of terminology. It implies that the sole function and purpose of the word in question is to 'determine' something that comes after it. That is 'sealed system' thinking.
In fact, to take 'my' as an example, in say, 'My table is red', the function within language at that moment is not simply to 'determine' something coming after it. It is to indicate possession (thus the old 'possessive' word at least has the merit of saying why we have the word in the language.) However, it is also doing something 'cohesively' i.e. in helping words stick together: it is referring to whoever is the 'me' who may e.g. have appeared earlier in the text or, in the case of a conversation, may be present as 'me' outside of the text in 'real life': 'my' will nearly always refer to these 'me's prior, or exterior to that phrase.
That's why humans invented this bit of grammar.
I would suggest that most of the 'sealed system' grammar is deadly boring to most people precisely because it is abstracted from everything that is interesting about language! Of course, some people are fascinated by sealed systems of anything. There is a fascination in trying to deduce a code from something that is not saying 'this is my code'. It feels like insider knowledge, only known to the priesthood.
Even better, you can then use it to test children and prove that some are cleverer than others or work harder than others and you can entrap them in useless and ambiguous tests in which the terminology of the sealed system is itself all over the place.