Scraped content is one thing, but most APIs require a unique key. Forget "trying to get to you": they already know everything they need to know to cut off your API access.
Break their mobile apps. Use their own API key against them. Also break their websites.
For example, for Google, look at Google Keep – that one leaks API keys directly in the list of accessed URLs, the key has been the same for years, and provides access to Maps and Keep. Same with YouTube (the app packages an API key for the v3 data API) or the WolframAlpha app. Many more apps, from simple "what’s for lunch at my uni’s cafeteria" to Transit apps all leak API keys. Preferably you use the key of an app from the same company which maintains the API, so you can guarantee to always find a recent one.
I spent a few weeks last summer extracting API keys for next to all services out of apps, and breaking some DRM solutions, just to get experience with reversing software (which was something I had a course about at uni at the same time, and the experience helped me with homework).
A rotating schema of pirated API keys seems even less sustainable than just risking use of a proprietary API. Not something on which I'd want to build a business either. At some point, the effort of reverse engineering exceeds that of actually building the damn thing for yourself.
The reverse engineering can be automated (as the official apps have to use the key at some point), and as the official app won’t get cut off from support, you can just continue using the latest version of it.
Yeah, but you can usually acquire an network of API keys without making the connection obvious (depends on their API access policies of course) and rotate them as appropriate. Also, many APIs offer the same data through a public interface that can be accessed by scraping, so you can scrape and avoid identifying yourself.
