SQLite requires that the self-reference be in the top-level FROM clause of the recursive part of a recursive CTE. PG apparently allows the self-reference to be down inside of subqueries, as long as there is only one reference.

I have make a copy of the Collatz Conjecture CTE that you linked to and was going to see if I could get it to work in SQLite for the next release cycle. I don't (yet) see any reason why it shouldn't work to have the recursive reference down inside a subquery, as long as there is only one recursive reference. No promises. We'll see how it goes.