I think Dave A explained it very well.
I am not doubting your abilities or questioning you intelligence, Kalmiya117, but racing tires can mask some suspension problems (inefficiencies, and definitely quirks).
Think of this example: A low horsepower car, tight, twisting track. The car will probably never get up enough speed to push racing tires to their limits. The car will feel "perfect". Put on some comfort softs and now the car can reach the tires limits and suddenly is understeers.
Another example: Mid-engine light weight car, coming into a tight corner from a high speed sweeper (decreasing radius). With racing tires you might have enough grip to pull this off with ease, put on sport hards and you get lift-throttle oversteer.
Both of those examples could benefit from some suspension tuning and without using the tires with less grip you would never have know them, or worse, you would finally get the low hp car on a track where it can get fast enough, or get the mid-engined car into a corner on another track and suddenly find the problems.
For the OP, I find that the sport soft tires feel a lot like the shaved Toyo Proxes RA1's I used when I raced (admittedly a long time ago). They are a street legal tire, but they are used for racing and have great grip.