Sure, go ahead and find an instance where I signed an agreement that included the explicit statement that said I was a neutral third party. Any agreement that I entered into stated that funds would be kept secure until goods/currency was received by the other party. That is what happened.
A contract does not need your signature -- certainly not in the US. And my argument is that the dictionary and legal definitions of escrow are controlling, as opposed to your imaginary definition:
By the very definition of escrow, and the common definition used on this forum, it indeed is implied that an escrow is a "neutral third party." You know that's how the law (and logic) generally work, right?
It's not a rational argument to say: In spite of the dictionary definition and commonly accepted use of the word "escrow," it is fair to assume that one that seeks the services of an "escrow" is not seeking a "neutral third party." You are the one that is incorrectly assuming, in the face of customary language and practice.
I'm also at a loss for how "funds would be kept secure" when they are being held by the interested second party. What's to stop the interested second party from taking the money and running? He has an interest in doing so.
Why would a trader ask for an escrow, otherwise?