I am going to say that I like this one but there are some issues to work out. If the laptop is in your lap in the first place it generally means that there was no where to put a monitor. BUT! If in replacing the keyboard area with a generalized counter balancing weight you might be able to over some of the issues that this set up would cause. The biggest being lack of usability compared to the current laptop models. I hate roasted nuts as much as the next guy but I am not sure the monitor described would sit up correctly as I typed in bed. I will keep thinking about it.

They don't call them laptops anymore because of the neat.

I invented a device called the "relatively thin box with holes cut in it" that I once used as a buffer between my laptop and my lap. I've recently invested in a "small piece of plastic with two fans in it", which is handily powered via a USB cable. Despite my having solved the problem already, you are on to something with the "screen jammed on the side of a computer case" idea.

I am highly concerned with the population growth in the world, and have decided to do my part to curb that growth where possbile. Therefore, I use my laptop on my lap whenever possible.

The major heat producers of a laptop are the power supply, CPU, and battery when it is charging. Everything else can stay below the keyboard. I would suggest creating a bump behind the hinge point of the display and house the power supply in that volume; this raises the heat source off of the lap. Move the battery in front of the keyboard under the wrists for weight balance. The CPU has so many pins it is difficult to route the traces unless the CPU is adjacent to memory and other supporting chips.

The heat sink of modern CPUs are very large, heavy aside, they are big. One possible solution would be to use a "heat pipe" to route the heat produced by a CPU through a flexible tube or rotary fitting, up into a flat profile heat exchanger with a separate fan in the display. The heat exchanger would add some weight to the display, but if it's profile is kept as close to the hinge as practical, then it should contribute to a low center of gravity.

But that would isolate the heat from the person while the computer is on their lap (while not being charged) and still have the balance needed to sit comfortably on the lap.