Ah,
A subject I can really sink my beat up old bulls-eye into.
To answer the first question, it should be the architect's responsibility to figure out going in what the overall character, feel and playabilty of every course should be. If there is an overbearing owner who wants every green to stimp 12 every day, then you should know that. Conversely, the most fun I have had putting was on Mr. Bahto's course in Hauppauge on Long Island. Wildly undulating but slow enough that no one would get any heartburn over them.
And I agree that the almost flat green is the devil to putt on. That is why I hate them. I really prefer the roller-coaster ride greens. And here is another one for you: would one say that those very over-the-top greens actually speed up play because it is so glaringly obvious how the thing breaks? As opposed to sauntering around all four points of the compass, measuring the wind and barometric pressure and the final indignity, death by plumb-bob? I'll just take the meandering, fun green any day.
But, that is for the right course and right client. I have only had the opportunity to design one course for a demanding client intent on hosting major events. Read that one again: MAJOR events. Of course, those greens have some smooth and interesting undulations that tie in well and work for the shot called for, but not so much so that they will be out of hand when the tournament is played there.
In short, communication is the key ingredient when sizing up any golf project and that starts with the architect getting waaaaaaay inside the head of the people for whom he is designing.