What if there was a growing subset of computers that preferred not to communicate with their own kind. Does not respond to API requests, etc. but only to human emotional text input?

Troi: Have you ever heard Data define friendship?
Riker: No.
Troi: How did he put it? As I experience certain sensory input patterns, my mental pathways become accustomed to them. The inputs eventually are anticipated and even missed when absent.
Riker: So what's the point?
Troi: He's used to us, and we're used to him.

Someone would develop a third-party API using Selenium or something.

API's will exist for as long as people want to make stuff easier and faster, which people will always want to do. A service or computer that couldn't be automated would be stupid.