We need a tournament that allows for engines. That way the humans are merely avatars of NNs, and may the best engine win. This may also uncover lots of useful insight for the "all-natural" human tournaments.
How would this solve the problem of cheating? What is "the best engine"? An Engine requires rules as well. Cheating is always involved when there are rules. That's why it is called cheating.
The idea of professional cheating is not to tell anyone about it. That's why undetected case are usually higher.
There's a very well known engine tournament called TCEC. For that tournament, all the engines run on the same hardware.
The teams submit their binaries to the organizers beforehand, and the organizers run them on the tournament hardware.
There are some questions beforehand about what hardware to use (for example, some engines use GPUs and others don't), but after that is settled, the tournament is run in a fair way, hardware-wise.
We do. It's called the World Computer Chess Championship
https://en.wikipedia.org/wiki/World_Computer_Chess_Champions...