Even a fully loaded full tower will weigh less than 50lbs so it would have to be a pretty wobbly desk to collapse under that weight. My desk has a slot or cubby hole I slide my tower into. The desk came with a door for this slot, but I removed the door to allow for unrestricted air flow.
A case, IMO, is supposed to sit quietly and discreetly out of the way. So I don't want it on my desk taking up space, nor do I want my ears next to the case fans. If my desk did not have this slot to slide the case into, I definitely would put the case on the floor - which is where all my other computers sit. Just make sure it sits on a hard surface to let air get under it and not a rug.
The opening is 24" tall in my desk and to make room for all the cables in back, the desk sits about 3 inches from the back wall. And as I noted above, I took the cubby hole door off so no problems with heat. That said, I always keep watch of my temps with CoreTemp.
I have quiet fans too but when you consider the CPU fan, at least 1 and probably 2 case fans, potentially a graphics card fan (or 2) and at least 1 PSU fan (and maybe a chipset fan too) even with quiet fans, they still reverberate through the case and can be heard when next to your head. I have a nice case too, but once you've seen it, you've seen it. I really don't want it drawing any attention to itself so I can pay attention to what's happening on my monitors.
