I think it's fair to say that you should highlight that upfront in your webpage because it's a more clear pain point than building other parts of backends.

Good point! We should do that :)

My two cents: in my experience with integrations there are many issues that you can't control yourself because third-party APIs are buggy, incomplete, etc

Yes, I have actually spent a large portion of my career building such integrations and Specific has grown out of that. In my experience, working with specifications makes it much easier to focus on the behaviour of the API you are integrating with, instead of the code architecture or boilerplate behind your integration.