"Why is it that the mechanism is "one parry can do what it wants unless the other party complains" instead of "one party can only do what it agreed to"?
Because that concept is consistent with all of US law -
See third party standing, third party beneficiaries, etc.
In the US, you usually can't raise claims on behalf of others, whether they are constitutional, contractual, etc.
This was not a surprise to anyone involved - the US, SBF, the bahamas, the lawyers, etc.
They are all quite aware of this.
You can argue this mechanism sucks, or is bad, but the answer to your question is because that's what all of US law says everywhere - this is not some unique feature of extradition. It's a core concept common across both civil and criminal law.