You wrote it's enclosed so the heat can't get out. As described it looks like a bad idea.
I just got a new desk and it has an enclosed cabinet on one side big enough for my tower.
The tower is about 17 inches deep, 7 inches wide and 16 inches high.
The cabinet is 23 inches deep, 14 inches wide and 21 inches high with a closed door.
It's a stock HP Omen, Intel i7 chip and liquid cooled, but I'm not sure if that would make difference in an enclosed space.
It would be incredibly convenient, but I don't want to overheat it and I think the graphics card (Nvidea GeForce GTX 1080) may still be air-cooled.
Is the convenience and less cluttered desk worth it?