arXiv:2609.12746v1 Announce Type: new Abstract: Agentic pipelines for structured-query generation are rapidly expanding, but it is unclear which part of the loop produces the gain. We use LAST-CQ -- a five-agent, training-free, execution-grounded Text-to-Cypher framework -- as an instrumented testbed, running three counterfactuals over 2,471 live-database queries and six backbones spanning three vendor scale tiers. Removing correction is worth between 3.1% aggregate execution-BLEU against the single-pass system and 12.3% against a no-refinement counterfactual (up to 80.7% for the weakest backbone). Replacing schema-grounded, LLM-synthesised feedback with raw database error strings costs almost nothing (20.9% vs. 19.9% naive exact match;