More generally, it's not clear to me why we should need to look inside lateral PHVs in the first place. Wouldn't the lateral PHV itself serve fine as a cache key?
Do you mean we use the lateral PHV directly as a cache key? Hmm, it seems to me that we'd have problem if the PHV references rels that are inside the PHV's syntactic scope. For instance
select * from t t1 left join lateral (select t1.a+t2.a as t1a, t2.a as t2a from t t2) s on true where s.t1a = s.t2a;
The PHV references t1.a so it's lateral. But it also references t2.a, so if we use the PHV itself as cache key, the plan would look like
QUERY PLAN ---------------------------------------- Nested Loop -> Seq Scan on t t1 -> Memoize Cache Key: (t1.a + t2.a) Cache Mode: binary -> Seq Scan on t t2 Filter: ((t1.a + a) = a) (7 rows)
which is an invalid plan as the cache key contains t2.a.