It feels like building humanoid robots so they can use tools built for human hands. Not clear if it will pay off, but if it does then you get a bunch of flexibility across any task "for free".
Of course APIs and CLIs also exist, but they don't necessarily have feature parity, so more development would be needed. Maybe that's the future though since code generation is so good - use AI to build scaffolding for agent interaction into every product.
I don't see how an API couldn't have full parity with a web interface, the API is how you actually trigger a state transition in the vast majority of cases