Leaving the game running like that seems like a sure-fire way to break the console.
Back in the day, when I still played the GTA 3D era games on my PS2, I wanted to play as Tommy Vercetti in Liberty City and Claude in Vice City. I still want to play a game like that where all of the cities are combined, almost like a remake of the original GTA but without load times and long stretches of roads in between Liberty City, Vice City and San Andreas (Los Santos, San Fierro, Las Venturas).
Even better if you could cycle between the different years, from 1983 (Vice City Stories) to 1995 (Liberty City Stories) and 2001 (GTA III), to see for example how Vice City looked later on.
Actually, there's a mod similar to this (includes Bullworth) though a noticeable issue is how the player character appears shorter than he should in different locations. But just the thought someone even attempted to do it is appreciated.
This is quite amazing, on the second video you can see that the console tries to render both games at the same time. If you could actually plug the TV cable to a customized hardware demultiplexer, like something implemented with a sixth generation FPGA—those are being used as AI accelerator, they are truly great—, you could probably play both games at the same time.