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.
I'm sure this observation has been made plenty of times before: a principal can gain negotiating power by delegating negotiations to an agent, and restricting that agent's ability to negotiate.
For example: If I'm at a family-owned pizza joint, and I want a slice of pepperoni but all they've got is meat-lover's, I can negotiate for the latter at the price of the former. This is a good deal with well-aligned incentives, and is likely to be accepted. But at a chain restaurant, the employees are not empowered to negotiate: It's the menu prices or nothing. Since I'm aware of their lack of power, and my demand for pizza is not very elastic, I'm likely to give them the higher price.
If I squint, this looks a lot like a precommitment, on the part of the pizza store, not to negotiate prices. But if they explicitly made such a precommitment, it might turn off customers -- nobody likes to feel like they're getting a bad deal, and a statement of precommitment (e.g. a sign reading "all prices are final") is likely to make customers feel marginally negative towards the business by drawing their attention to the money they aren't saving.
By contrast, the corporate form -- such as the chain store has -- gives this kind of 'precommitment' as a side-effect of the otherwise socially-normal behavior of delegating limited responsibility to employees. Same benefit, but without the drawback, mostly because the practice is socially-accepted.
Is there any literature that covers this kind of thing further? Particularly the link between precommitment and agents with limited negotating ability.
(I am sitting in a chain pizza store as I write this. Guess what I wanted to order, and what I got instead?)