I want to know everything about the 4L60e, but i dont know much and have not rebuilt one yet. My burb has a shift kit, I believe its transgo but I personally wouldnt know the difference from oem components. If I put my peddle to the metal my Burb will get up and go, light the tires right up and I can absolutely feel every shift as they are quick. A shift kit makes the shifts happen quick so as to create the least amount of friction possible and its felt like snap? Quick and not very smooth. Friction kills trannys. My Burb is a heavy truck I wonder how that stage 3HD Tranny would operate in a pick up, probably tonnes of fun and when the sierras trans blows I'm dropping it off to be rebuilt the same way by the same race shop who's been in the business for over 50 years.
If I'm driving my truck normally and taking it easy I can feel the shifts but they are not rough at all.
Since theres many different shift kits it sounds like your truck does have one and its probably set up for drag racing, peddle to the metal style, wide open throttle.
But I'm far from an expert and would think if your chirping the tires while taking it easy there "may" be a problem.
I'll do fluid n filter changes and everything else on my truck, I take my transmissions to the experts for diagnosis, tuning and work. The only way to know for sure would be to have an expert look at it or study the many possible shift kit options and compare to what you have.
Heres transgos 4l60e section....
https://transgo.com/products/4l60e-4l65e-4l70e/
Al