Laying doors flat to paint is okay(?) if you have one or two doors. I painted six doors, both sides, last night. One of them needed two coats both sides. In an office, where would I have laid them? On six sets of sawhorses? I couldn't have done both sides if they weren't hanging, not in one night. In all my years I've only painted a couple of doors flat, but for none of the conveniences or necessities mentioned. Not trying to belabor a point, but don't want an inexperienced HO to think it's necessary or even a better way, it's not.
Over applied paint will run and sag on a hanging door, but it will also puddle on a flat door. Properly applied, the paint will hang and level out on a hanging door.
A flat door is a greater dust magnet than a hanging door.
Working over a flat door has a greater risk of a drip from the brush hitting a finished area and getting missed or having to be brushed out creating a mar.
And the amount of handling involved in hanging a heavy door with soft paint could necessitate a possible recoating after hanging. And if you get deep fingerprint impressions on a sheen coat, good luck.
It's not worth it.