It's worth mentioning that part of the reason cheating isn't so common on consoles is the big popular shooter esports aren't console games. In your theoretical scenario, you'd also need to acknowledge that the large hacking community that focuses the majority of its efforts on PC games would switch to your console games. This would inevitably increase the prevalence of cheats on consoles. Would it necessarily make cheating quite as common? Maybe? It's impossible to say. Whether cheating happens on console is partially a big dice roll on whether hackers decide to devote enough energy to your platform. Nintendo puts real effort into their security, whether you believe it or not, but people like hacking Nintendo consoles.
I'll also address the real point here. Cheating is not the biggest issue in the world. I've been PC gaming for a decade at this point, and I've seen hackers in my many hours in Counter-Strike, my shooter of choice. But cheating is not universal, or in every game. Especially with recent efforts like Valve's Prime and Trust Factor, I barely see cheaters anymore. And as someone who has done hundreds of Overwatch cases, I am well aware what a cheater looks like. Even pretending that cheating is a universal issue that ruins PC gaming is overdramatic. PC games are the biggest games in the world, despite cheaters. The reason why they have cheaters
is because they're popular.
If you want to eliminate cheating, if that's your number one goal, the only logical end point is game streaming such as Stadia. There's literally nothing else that will work 100% of the time. As long as the game code is running on a machine that a cheater physically has access to, cheating will exist. And personally, that's not worth it. I don't even mean the quality issues with streaming. I mean the lack of software freedom. Modding? Dead. User file access? Dead. Software archival? Dead. Backwards compatibility? The games only last until they're removed from the service, like when Netflix's contracts end. And all of those points I mentioned apply mostly to consoles as well. Most PC gamers don't only care about graphics or framerate. The platform is free, open, and gives control that users want. And Steam is competitive with PSN and Xbox Live, so clearly it's not an experience people aren't willing to deal with.
If you want an idea of how reverse engineered consoles have been at this point, here's a talk on reverse engineering the PS4
from five years ago.