Bernie, after reading Rikki post I went back and reread your first post. Studies like scales and arps. are mainly used to give freedom of movement. To make your hands move without too much thought.

When I started taking piano lessens I and watched my Dad playing the piano, I had the same question as you – thumb under, ect. His right arm moved frequently, positioning his hand, rarely tucked his thumb. Fingers 1 2 3 4 were used, 5 when needed.

I took traditional piano lessens for a short while. What did I learn? I learned that I was having no fun.
I found a teacher who had a different approach. I started with learning how to voice and play two hand chords; both traditional and jazz. Which notes were important, and which notes were the color tones. Then I applied what I learned to playing melody and chords from a lead sheet. Now I was having fun.

For ballads and some up-tempos, it was great. For polkas and fast-moving music; back to scales and arps.
John C,