The answer is pretty simple if you think about it. E-signature works because we are ....
Capturing the "intent to sign" and tying that action to a system generated log that connects the signing "event" to some piece of "personally identifiable information." In other words, something that helps indicate that the event is tied to a specific person.
Without at least a valid, unique email address that's owned by the person signing, the process is pointless.
Yes .... you can use a "generic" email address, but should you?? Not really.