Connor,
Great insight and I completely agree with you.
Separating API testing and development leads to silos. The point I tried to highlight here was API testing should be considered a practice rather than a thing done by a role such as a QA person.
In small projects, I've seen the developer writes the test himself. That's a great way to start. But when the project evolves over time, some specialized testing is inevitable. For example, compliance testing, security testing, etc. Hence, it's good to assign the specific areas to specialists.
Having said that, this shouldn't be done from the day one of the project. Once the API reaches a point where you think expert input is needed for testing, you can branch out. But the beauty is. that all teams must conform to the API spec. That doesn't lead to making silos.