Hypothetically speaking, would you be willing to attempt to set it up?

If someone were to do it, wouldn't it defeat the whole purpose of the system by answering "yes" to this question and letting the backdoor users know that someone is now laying traps to catch them using those backdoors in the act?

However, the effort of setting this up could be better spent on making (or contributing to) a messaging app that's open-source and secure by design, where you don't need such setups to detect backdoors because they are near-impossible to introduce (open-source code and lack of a central server).

And the most likely thing to happen is that after you have spend years creating it nobody would use it.

It was completely rhetorical question. I implied no one would take the risks.

There are people willing to be a tor relay I bet that kind of people would be willing to help to an extent.