I think the basic issue is that ADTs are simply not indexed--so to the degree that you write a query that would necessitate an index on a subtree of an ADT, you will face asymptotic blowup, as the way ADTs work will force you to scan-then-test across all ADTs (associated with that top-level tag). The issue is discussed in Section 5.2 of this paper here: https://arxiv.org/pdf/2411.14330
I think the basic issue is that ADTs are simply not indexed--so to the degree that you write a query that would necessitate an index on a subtree of an ADT, you will face asymptotic blowup, as the way ADTs work will force you to scan-then-test across all ADTs (associated with that top-level tag). The issue is discussed in Section 5.2 of this paper here: https://arxiv.org/pdf/2411.14330