Any reason not to run my Macbook Pro upside-down in clamshell mode?

You can place the Mac in whatever orientation you like during clamshell mode as long as it's supported and protected from falls.

I really like the Book Arc stand so that the trackpad area is by the table and all the warmer section near the hinge is up and exposed on all sides to airflow. If you really need maximum cooling, try the SVALT D cooling stand.

Your proposed mechanism should be measurably cooler when you have the CPU generating maximum heat and for some reason the airflow / ambient temperature wasn't cooling things as much as you had hoped. The air trapped in the LCD panel can have a fairly good insulation value and if the surface is soft, airflow under the feet is diminished.

The Apple fans are high quality and likely magnetically suspended or have so little play it's not a concern unless you have shocks or other accelerations.

One reason I can think of is that while the bottom is protected by rubber feet, the top is exposed. While you may think the surface you're placing your Mac on may look clean, it's possible that there's some grit that will scratch your Mac when it moves. A non-slip surface might mitigate this somewhat, but you may also want to invest in a skin to protect your computer.

The heat is unlikely to damage the screen (I've run mine in clamshell mode for a long time) and I'd be concerned about damaging the finish.

An alternate solution: If you have the room, open the laptop and place a magnet on top of the case near the batter meter or auto port area (I don't know exactly where the sensor is on the retina but that's where it is on my MacBookPro8,2). It will think the lid is closed while still allowing for vertical convective and radiant cooling.

If heat is your concern, I recommend the Griffin Elevator Stand. I use it personally and prefer it over my previous laptop stands because of how exposed the underside of the laptop it is. 2 (rubber padded) metal brackets are all the block the bottom of the laptop, allowing for great air circulation.