An API has to make money somehow for its sponsor. A major e-commerce platform adopts an API that allows its developer ecosystem to build apps that enhance its user experience (UX) and reduce friction in transactions. Check out eBay's developers program for examples of APIs that broaden their platform's appeal. We publishing platforms deploy APIs so their channel distribution partners have additional means of sharing their content. NPR's API is one example, and that API's creator reveals on ProgrammableWeb how it creates revenue opportunities among very focused target audiences.
The US federal government's extensive API collection at Data.gov don't bring in extra tax revenue. They make it easier for businesses to manipulate the government's public data into formats their customers can use. I suspect there's an untapped market among government IT contractors for services that clean up dirty data. They can tap that market if they figure out the APIs that lead them there.
API monetization is probably a tough road to travel for stand-alone developers. Most large enterprises seem to open their APIs to developers for free. A free tech giveaway encourages adoption. The apps employing the API can make money through in-line ads or e-commerce fees. I think independent software developers who focus on creating APIs for enterprises can make money on a contractual basis. This does not mean the API itself is a stand-alone money maker akin to a retail portal. It means API development is a specialized niche. API developers who insist on placing the most desirable features behind a pay wall risk being shut out of an ecosystem if users fail to adopt. Freemium APIs that showcase a developer's quality may be the best way for IT contractors to build a portfolio of work.
Alfidi Capital does not have any APIs available for download. This firm maintains no client data, performance data, or any other kind of data that developers could ever use. The analysis you see here is data-driven but that data is all in the public domain, linked where appropriate in these blog articles. I don't have the computing skills to throw APIs at the public. If I did, I'd deploy an API that enables female tech developers to share photos of their hot bodies with each other and me. That day may never come, so techies will just have to launch APIs at each other and hope some major platform adopts one as its standard.