This is kinda out there but I would like to hear some input on the matter. Is it generally a good idea to put a PC in a desk like this? I have a desk that has a space like this one for a computer and that's where I keep my old Dell that I have now, but when I finish my build I'm not sure I wanna put it in there. Is it bad for cooling or does it really make that much of a difference??
That would be bad for cooling. However, it wouldn't matter too much if you left the door open when using the computer AND didn't do any overclocking. If you plan to overclock, I would be wary of leaving the computer there without much airflow.
This also might be kinda out there ... but you could always cut a major portion of the door panel and replace it with silk screen or something that would let air through, but still look nice ... and make sure the rear of the cabinet is open or at very least well ventilated.
You could even consider opening up the underside a bit as well so air can flow underneath if you have any fans/entry/exit slots on/near the bottom of your case.