I'm a new pilot, so it's possible I have misunderstanding here, but what I figured out (at least for general aviation) is that IAS/CAS are used to monitor aircraft behavior/performance characteristics, and TAS is used primarily for navigation.
Imagine two scenarios when you are flying in dense air and in thin air: To generate the same lift, the aircraft has to move faster in thin air so TAS will be different, but in my understanding if your aircraft generates the same lift, you IAS will be the same. As such regardless of TAS, IAS/CAS show you how your aircraft is currently preforming as if it would be flying with the same IAS at sea level at standard temperature, which includes stall speed, flaps retraction speed, etc..
Imagine if you'd manage to fly your Cessna on Moon with no air pressure at all. Because:
Because the air density is extremely low, almost zero, but there are just a few molecules of gas on the entire moon nonmatterno matter how fast you'd beyou're moving:, your IAS would be showing 0 because there is no pressure on the pito, there would be no lift as well, nonmatter. No matter how fast you'd beyou're moving against those few molecules of gas (which is TAS), you plane would fall like a brick, and IAS would be telling exactly that, as it would be showing 0. This is why you use IAS/CAS on takeoffs, landings, because you need to know when it's going to stall.
TAS on the other hand has nothing to do with the aircraft performance, it just shows how fast youryou are moving in a body of air and withby applying wind corrections you calculate GS for navigation planning in calculating time in flight, checkpoints, etc. I don't even know if TAS is needed in flight if you use GPS with ground speed. Guys, who know what else is TAS for in flight if you have GPS, please share.
The one thing I don't really get is what actually has more impact on aircraft performance: IAS or CAS? Let's say on cessnaCessna with one static port on the right your IAS will be noticeably different between left and right slips because if your aircraft is turned to the right, it's left side witwith the static port will be more exposed to upcoming airflow which will be pushing on static port reducing differential pressure and as such IAS will be lower, and if it's turned to the right, the opposite will happen: left side will be hidden from the airflow and will be in the thin air increasing diff pressure and showing higher IAS. So aircraft performs the same or very similar in the left and right slips, but IAS will be very different.
And I don't remember how flaps effect on IAS/CAS difference, but something tells me that CAS is more accurate speed that shows aircraft performance then IAS.
Please add your comments who knows!