As I stated in my comment/question below your question, it seems that you are "abusing" (mis-using) the phrase "abuse of notation."
In mathematics, abuse of notation occurs when an author uses a mathematical notation in a way that is not formally correct but that seems likely to simplify the exposition or suggest the correct intuition (while being unlikely to introduce errors or cause confusion). Abuse of notation should be contrasted with misuse of notation, which should be avoided. A related concept is abuse of language or abuse of terminology, when not notation but a term is misused.
In particular, I'm referring to your observation:
I understand if later on in one's studies if things are assumed to be in place, but there are plenty of textbooks out there assuming certain things are known before teaching them.
Here, it seems to me that you are complaining that you are encountering the use of notation that you do not understand and have not yet encountered, and for which the author/instructor has not explicitly defined. This is NOT an abuse of notation. This is where you "speak up" and ASK what is meant (if in class). Alternatively, in such a situation, you need to take the initiative to understand the notation, to look to see if the text in question has an appendix or index defining the notation it uses, or you can appeal to some reference to better understand the symbols/notation and its various uses, which are usually context dependent.
That said, with respect what actually is meant by "abuse of notation": we are all human, and mathematical notation, like any language, is subject to ambiguity, perhaps less so than natural language, but nonetheless, it is still subject to ambiguity.
Notation also provides a means to communicate, compactly, what would be laborious to try to communicate otherwise, even if at the cost of "abusing notation."
In any case, being human also means it's usually a good thing to avoid pedantry and to learn to tolerate the use//abuse/misuse of any language (mathematical or otherwise) by others. Certainly, you may want to it out when you take something to be an erroneous use of notation/language (and doing so in a helpful way), but deciding not to tolerate it is perhaps going too far.
And I suspect that we all take "short-cuts", when handy and when we can safely assume the notation we may be "abusing" will be understood. Certainly, there is a "fine-line" between taking advantage of notational short-cuts, and full-fledged "abuse" of notation that fails to convey what was intended by its use.