Follow one Tableau dashboard through a Tuesday. At 8:00 it runs its twelve queries, Databricks computes them, and the query result cache keeps the answers. At 8:15 it refreshes, and the result cache answers all twelve without recomputing anything. That is exactly what it is for.
But the warehouse had to be running to serve those hits, so the Auto Stop clock started over. At 9:02 a few new rows land in orders, and every cached answer on that table is cleared, last quarter's included. By evening the warehouse has been awake all day for a dashboard whose data changed twice.
Every Databricks cache did its job that day. None of them is built to answer from outside the warehouse, and that is the gap the gateway fills.
Whatever the gateway passes through still gets every one of these caches, exactly as it does today.