Should This Inventory Sync Actually Be a Streaming Pipeline?

A retail company currently syncs warehouse inventory counts to its e-commerce site via an hourly batch job. A new engineering lead proposes replacing it with a full Kafka + Flink streaming pipeline, arguing "streaming is the modern approach and will future-proof the architecture." The stated business complaint is that customers occasionally see items as "in stock" that sold out earlier that hour, leading to cancelled orders and complaints — but nobody has stated a specific target latency.

1. What question should be answered before deciding on an architecture at all, and how would you get a concrete answer to it?
2. Given the described symptom (stale in-stock status leading to cancellations), evaluate whether a full streaming rewrite is actually justified, or whether a smaller change could address the business complaint.
3. If it turns out the business genuinely does need near-real-time inventory (e.g., for a high-demand flash-sale scenario), what would change your answer, and what would the resulting design need to handle that the hourly batch job never had to?