The issue here is that you're using "locked down" too generically. What you actually want is something like remote attestation. The device can assert with a signature that it's running a particular version of the OS and a particular version of the game and in so doing allows you to know that the user isn't cheating by using some other software.
That has nothing at all to do with whether you can install arbitrary software on the device or who gets a percentage of what. Even if you could install the Amazon store on your PlayStation and the install Cheat App from there, the device wouldn't then assert that you're running the official game (because you're not), and then the other players would know that and be able to boot you out. You don't need the other player's console to refuse to install an arbitrary app for that, only for it to be able to tell you when that has happened.
https://docs.microsoft.com/en-us/windows/uwp/xbox-apps/devki...
Switching back and forth between retail and DEV mode is as easy as rebooting.
Of course you can now make the argument that any form of code execution increases the attack surface. And you're right but hypervisors can be quite effective. Also the XBOX One can be put in developer mode to run arbitrary UWP apps and has not yet had any major exploits (to my knowledge), where the PS4 has no similar features, but has had several firmware versions with significant security flaws.
This feels like losing options, not gaining them.
Freedom? No. Opportunity? Maybe. I think communities would arise to fill the demand though. Pseudo-anonymous reputation systems tied to matchmaking could fill the roll. I have a group of pseudo-anonymous friends/acquaintances I frequently play games with online. None of us cheat and if any of us did, we'd stop playing with them. We don't need big brother. We don't need technical solutions to social problems.