In sprint the starting 5 pieces aren't completely random at least, because the first piece is never a Z or S piece, and I'm like 80% sure that the first 5 pieces come from a pool of preset orders but I haven't completely confirmed this. I don't know if this is documented anywhere else

Just noted
Piece One - No S, or Z
Piece Two - No L
Piece Three - No I
Piece Four - No S, T, I (heh)
Piece Five - No T

It's definitely a pool of sets they pick from with newer Tetris RNG

This is mostly not right.
Piece One - No S or Z: This is correct, and I think it's reasonable.
Piece Two - No L: This is incorrect, I've gotten it piece two.
Piece Three - No I: Incorrect.
Piece Four - No S, T, I: Incorrect.
Piece Five - Not T: Incorrect.