"I can imagine people or companies can use this API to check their own functions in test cases"
Testing is one good application.
"But I believe this business doesn't trust anybody but well-known players or experts"
Take a look to the community mantaining quantlib.
"Also the time is essential so they will prefer a local library"
How long does it take to financial institutions to test all valuations for each modification to "local libraries"? Using external services could avoid that. This is not going to be the one, but it would be just a matter of resources to improve performance(ie big data platform for risk simulations)
"And again, the security can prohibit external APIs"
Why do banks rely on RSA for payment transactions but don't do it for other purposes?
"I don't discourage your work though, perhaps it is a step to your personal success, who knows"
Already did, I learned and enjoyed doing it :)