The multiplication nobody budgets for
One agent calling one internal API is an afternoon. The trouble arrives with scale in two dimensions at once.
Every agent that needs a capability needs an integration to it: the call, the auth, the schema, the error handling, the retry policy, and a description the model can use to decide when to call it. Do that per agent and per tool, and the work is the product of the two counts, not the sum. AWS names this directly in its Gateway announcement as the M by N integration problem.
Key idea: a gateway converts a multiplication into an addition. Each tool is adapted once, each agent connects once, and the integration count grows with the sum rather than the product. At 50 agents and 200 tools that is the difference between 10,000 pieces of glue and 250.

