> none of the big three consoles allow you to install anything you want on them.

The Xbox kinda does: https://learn.microsoft.com/en-us/windows/uwp/xbox-apps/devk...

And while unofficial, the Nintendo Switch has an exploit chain that lets you run native apps or mainline Linux/Android with Nvidia's Tegra drivers: https://github.com/CTCaer/hekate https://github.com/Atmosphere-NX/Atmosphere

So that's two of the big three consoles that technically do let you install anything you want.