Logic, not in this case, just messages.

The point of separate error streams echoes the main Unix philosophy of doing small things, on the happy path, that work quietly or break early. Your happy results can be chained on to the next thing and your errors go somewhere for autopsy if necessary. Eg,

    p1 | p2 | p3 > result.txt 2> errors.txt

will not contaminate your result file with any stderr gripes. You may need to arrange error streams from p1 and p2 using () or their own redirection. If it dies, it will die early.

BUT speaking of logic, the concept is close to Railway Oriented Programming, where you can avoid all the failure conditionals and just pass a monad out of a function, which lets you chain happy path neatly. Eg, nice talk here https://fsharpforfunandprofit.com/posts/recipe-part2/