From q=(rho*u^2)/2, it can be seen that if density is decreased, speed (TAS) must be increased to maintain the same q. Since IAS is (ideally) derived from q minus free-stream or ambient pressure, this equation indirectly shows the relationship between TAS and IAS.

So, you were not wrong when you wrote that TAS is used in stability calculations. TAS is implied, and so is IAS.

Pilots like IAS because it's what's in front of them most of the time. And it is a reliable indirect measure of q, which is something that can break airplanes. TAS by itself doesn't measure q, so it's not terribly useful to a pilot trying to out-climb a tree, or keep the wings on his mount during aerobatics or turbulence.