That's exactly why they won't let you store their response data. They want the data used to build apps to help consumers board their flights or get picked up on arrival, not benchmarking dashboards for third parties to assess on time performance and the efficiency of its baggage handling service, besides which the airport itself is likely subject to restrictive licence agreements for some of the data supplied in the API.

How would they even check?

I would imagine it's so that they could pull your access if they found you publicly sharing comparison data(rg how often a flight is delayed due to loading) or some such.