They do because you get to design the kingdom and exclude cards that make cards come back from the trash.
Good point, I didn't read the question carefully enough.
You cannot do infinite chains with those, unless you mean over several turns, which ITR isn't needed for and which isn't the point of the challenge.
As Procession is a tfb i admit that i made a mistake putting it in the "no use" category, though. Clearly it belongs in "limited use".
You can (assuming the right kingdom). Suppose 1 Rogue and 1 Scrying Pool is already in the trash, and you have a deck consisting only of action cards.
Process X, play it twice and trash it.
Process Rogue, gain X and Rogue
Process Rogue, gain Scrying Pool and Rogue
Process Scrying Pool, draw deck
Then we've played X twice, and we are in the same initial position: 1 Rogue and 1 Scrying Pool in the trash. And you've played X twice.