Me personally, I wouldn't do it. I have spent a little bit of time in old cars with no gutters and it sux. Have a closer look on some of the hot rods and mid 50's type customs and some of these guys have used a 3rd option. They cut the gutters off and weld a small diameter solid round stock in and mold it into place. The result is the smooth look and the roof goes far enough past the door frame etc not to cause a problem. I think it helps brake the line of the car up enough so it doesn't start to look like a bubble. It's a little hard to explain but when you see it first hand it makes sence.Gutters on old cars looks right.

I know what your saying about the various different methods that have been used over the years to change the look of cars and each really comes down to personal tastes. Older style cars tend to look like bubbles from little touches like removing the gutters and this then leads to the square door and window frames looking out of place, this just leads to more work of radiusing the corners of these etc. But its all done for the individuals tastes and to be a bit different.
Datsun door frames are tucked under the roof abit so this still gives definition of the body lines except a bit smoother without the gutter. ( To me personally )

New cars still have various forms of gutters except more aerodynamic. Like ang said the door seals have the gutter or on various makes of cars you will notice the widscreen is recessed down abit lower than the A pillars and this continues up into the gutters in the roofline. They do this to make a leading edge for wind as you drive or rain to follow along to prevent it or atleast minimise it coming in an open window.

As for driving with the window down in the rain? I always do for what ever weird reason I just always have it down, even driving home on a cold night I still have it down with the heater going. But in a datsun its a necessity to prevent the windows fogging up.

Phunk, you are so right. I had to have the window down in the XB (1974) because the demister didnt work and thats the only way you could stop fogging up, let a bit of water in tho.
Come to think of it, I was driving home from work tonight (6pm) about minus 5 degrees with windchill but I still had the window down and the heater just going in the new ute. Why do car enthusiasts do that? Most normal(?) people dont, but we do?

nothin beats warm feet but still the cold wind in your face