In hindsight, whoever gave my comment its initial "-1 point" ding was correct: although I thought "Why wouldn't you just rewrite your source code" was a flippant question that doesn't mean it deserved just a joking answer. So, some more serious answers:
Your delegates are more powerful because they are known to have fewer choices and because they are known to value those choices differently, which can prevent them from being subject to threats or affected by precommitments that might have been useful against you.
I wouldn't rewrite my source code because, as I joked, I can't.. but even if I could, doing so would only be effective if there were some way of also convincing other agents that I wasn't deceiving them about my new source code. This may not be practical: for every program that does X when tested, returns source code for "do X" when requested, and does X in the real world, there exists another program which does X when tested, returns source code for "do X" when requested, and does Y in the real world. See the concern over electronic voting machines for a more contemporary example of the problem.
Whether I would just not do something is irrelevant - what matters is whether everyone interacting with me believes I will do it. It's easier for a customer to believe that a cashier won't exceed his authority than for a customer to believe that an owner won't accept a still-mutually-beneficial bargain, even if the owner swears that he precommitted not to haggle.
Wild speculation: There are instances where evolution seems to have built "one-boxing" type adaptations into humanity, and in those cases we seem to find precommitment claims plausible. If someone is hurt badly enough then they may want revenge even if taking revenge hurts them further. If someone is treated generously enough then they may be generous in return despite not wanting anything further from their benefactor. A lot of the "irrational" emotions look a lot like rational precommitments from the right perspective. But if you find yourself wishing you could precommit in a situation where apes aren't known for precommitting, it might be too late - the precommitment only helps if it's believed. Delegation is one of the ways you can make a precommitment more believable.
Someone really should write a "Cliffs Notes for Schelling" sequence. I'd naturally prefer "someone else", but if nobody starts it by December I suppose I'll try writing an intro post in January.
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?)