The business case for APIs gets made badly most of the time. People pitch them as a revenue line, and for most organizations they are not one. The real case is simpler and stronger.
First, integration. Connecting a CRM to a billing system, wiring a payment API into a checkout, syncing data between platforms, automating a workflow that used to be four people and a spreadsheet — that is the work the business actually cares about, and APIs are how it gets done. The API industry has spent most of its energy on the producing side, and left the consuming and integrating side underserved relative to how much of the value lives there.
Second, awareness. You cannot expose a capability through an API until you have identified it, defined it, named it, and understood it. That requirement is a forcing function for organizational self-knowledge that almost nothing else in technology provides. Most large organizations genuinely do not know what systems they have, who owns them, or what data they hold. Doing APIs is how they find out, and everything else — governance, risk, compliance, consolidation — depends on knowing.
And then the discipline underneath both: an API has no value until it is actually used. Not until it is built, not until it is announced. Until someone integrates it and something real happens on the other side. Measure the integrations, not the endpoints.