While the question, whether it carries any responsibility, is speculative at best, I believe it's in the best interest of StackExchange, to do more to protect it's user privacy and as a byproduct, help itself in the process.
We have already established that sharing email address is not good for the community, even if it is what the user wanted, as it moves discussion away from SE to private. JorneymanGeek says
Likewise, an email, in addition to being a PII like, moves the information from SE and the commons to private messaging of sorts.
I'd consider this undesirable, as far as the goals of most sites go.
The case holds true for Google files in SE as well. Usually it moves the discussion away from SE to Google's inbuilt comments.
Yes, We are not 4 year olds, but accidents happen and there's a simple matter of ignorance. There are also precedents established by other Software companies like Github (and Facebook as mentioned by IMTheNachoMan). Github
Is Github used by 4 year olds? Why should they implement this feature? Because it helps users using it(and the companies, which provide the secrets)
In this case, it's trivial to detect whether there's a email address(or a Google docs link or password like characters) in a question and warn the user beforehand or explicitly disallow email addresses. The cost benefit ratio hugely favors implementing such a feature, especially with Stack Overflow.