How often are you shocked by grammar?
Although there is still some disagreement about the interpretation of the stems as tense or aspect, the dominant current view is that the stems simply represent tense, sometimes of a relative rather than absolute nature. There are some unusual usages of the stems in certain contexts that were once interpreted as indicating aspectual distinctions, but are now thought to simply be idiosyncratic constructions that do not neatly fit into any aspectual paradigm.
Tenses are pretty fundamental, right? Yet stems in Arabic have changed from being aspects (how the event occurred) to tenses (when the event occurred)!
Arabic hasn't changed. This shouldn't affect how we study the language, and it hasn't affected how Arabic speakers communicate.
I love this example because it shows the difficulty of fitting the inherent messiness of languages into sharply defined grammatical classes.
Even classifying words can be fuzzy. 'Mammoth' was originally a noun. Speakers began using it metaphorically ("a mammoth project") and the meaning eventually focused on size. 'Mammoth' is often an adjective today meaning large rather than hairy.
Rigorously focusing on the classification (is it a noun or an adjective here?) can hinder learning.
Grammar is great for increasing your ability to write new sentences (beyond reusing set phrases). It also helps understand ambiguity. Ultimately, it must be subject to our end goal, which is to communicate.
Grammar is massively emphasised when foreign languages are taught in schools. It's easy to fall into a habit of trying to absorb terminology which isn't helpful for learners.
Make grammar work for you, not the other way around!