I can't tell you how much time I've lost to the porcelain throne! (I never measured it) but I do know that I want to get ahead, and when I get to do a crap in a cubicle with a door, I'll have made it!
P.S. This is why wifi and laptops are so great. A lot of thinking time can be had on the dunny. To really get your creative juices flowing, encourage your employees to think about direction on the bog. You could get your next Gmail there. Think of it as 10% time, without need to allocate the 10%. Your employees will thank you!
If its a quiet-low-traffic work environment, then open door is perfectly fine, but if not, then it won't provide the quiet that a closed door does. I don't care about privacy, I care about (lack of) noise and distractions.
My ideal setup would provide a communal quiet library-rules room with couches; sound-proofed meeting rooms with doors; breakout areas for groups to sit and talk; hot-desking space; and 1-man offices with doors. Then allow people to use them as preferred or necessary for the work they're currently doing.
Failing that, at a minimum have open-plan + plenty of silent "library rules" space.
> "when you'll get better, you'll get that door"
So, you want to sabotage my work quality until I produce better quality work?
EDIT: Forgot to say that movement (seeing people walk past out of the corner of your eye, for example) can be just as distracting as noise.
Then I'd use them as some kind of status token, to gamify things a bit. Mangers would have offices with doors by necessity, for private conversations with employees etc. And for the rest, if you are a lead developer, or tech lead or senior developer, than you get a door added to your office. Otherwise the hinges stay, but no door... like a hint of "when you'll get better, you'll get that door" :)