Your delegees are more powerful because they have fewer choices? Why wouldn't you just rewrite your source code to eliminate those options?

Well, you are more powerful because your delegees have fewer choices. "Delegate negotiations to an agent with different source code" seems equivalent to "rewrite your source code" (assuming the agent can't communicate with you on demand.)

Actually, it seems possibly even more general, since you are always free to revoke the agent later.

As to why the agent would react differently: all other things being equal it wouldn't. However, we do have the inbuilt instinct to go to irrational lengths against those who try to cheat us, and "corporation delegating to an agent" doesn't feel like cheating because it's standard. I suspect that "precommitment not to negotiate", depending on how it's expressed, would instinctively look much more like a kind of cheating to most people.