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It would be fantastic and very relevant to use Piwik as a API Analytics service. Piwik with its powerful log analytics and import can provide great insights in monitoring API and web services, such as: API request counters, successful requests, requests with errors, API Performance measurement, Continuous API monitoring. Count how many users use the API, which users use it often, which parameters they use, etc.
We would like to think about this use case a bit more and document how to use Piwik as a API Analytics platform. We have ourselves two APIs we could track using Piwik as a start.
See also #5257 Application Performance Management & Monitoring