This is the right framing: once an agent can move money or sign something, it's not a tool anymore, it's an actor — and actors need to be identifiable. The plain test for a small business is simple: would you let an agent you can't identify act on your company's behalf? No.
Your caveat matters too. A credential that only works inside one vendor's garden is a username, not an identity. The interesting question isn't just whether agents get IDs, it's who issues them, who can revoke them, and whether the ID follows the agent across systems.