Hello!
I agree with what next in that it's good to keep in mind the big picture and that's mostly how I try to approach the questions in the aerodynamics/flight mechanics section ...
Know the order of magnitude (or the "power of ten") and where to look up the details or what tool to use to compute them and you will be fine. That's what they told us back at university and it served me well, both for engineering and for flying.
Sometimes one over-simplifies this way (my memorising the speed of sound as 1000 km/h rather than the precise value of 1235) but for me it was good enough to get more then the 75% of correct answers required in the exams
And why would I want to know my TAS? IAS is all I need in terms of aerodynamic performance, right? And GS is what I need for navigation? Right? Wrong?
Right. In the aeroplane I fly at work, the TAS is displayed in the lower corner of a secondary display and I swear that I didn't bother to look there for the last 1.000 flying hours (maybe it has vanished from the display in the meantime, who knows?). Totally irrelevant. You could compute your GS knowing your TAS, but then you must also know your exact wind. At any moment. Nobody does.