I always thought it might be neat to include one dead flat green on a course, something with a very small green that's on a little hill so drainage isn't much of an issue. I think it would drive people mad to look for a break that isn't there, and might drive them even more mad if they knew it was dead flat because they'd know their misses were their own fault!
But the place I think no one could argue that should have a dead flat putting surface is half the practice putting green. Courses always try to make their practice greens so "interesting", and that's fine, but leave us some area where the only target we have to worry about is the hole. Drainage need not be a big issue there, if that part doesn't drain well after a heavy rain, just close it. Or have two smaller practice greens, and close the flat one when necessary.
Wouldn't work for grasses that have a grain, of course.