Obviously maintaining a flattened version is going to perform better in queries, but you're trading maintenance (write) time for query time. Or materialization time if you decide to do it lazily.
A->B
A->D
B->C
C->D
Postgres will walk both paths from A to D in the recursive CTE and then you can filter them afterwards to keep only the shortest.
You can use aggregate functions within the recursive CTE, so you can’t GROUP BY your starting node and stop once you find the first path. There isn’t a way to compare across multiple paths or iterations of the for-loop.
If I'm traversing ancestors (let's say) until I find one that doesn't satisfy a condition, it'll bail out then. I get that this doesn't serve all uses cases, but it isn't a small thing either.
> The solution is to build and index denormalized n-th order relationship tables.
This sounds much more performant but also more difficult to maintain.