elihu - It's almost impossible to say if a 3 speed would work for your situation. Too many unknowns. How many miles, how hilly is it. But keep in mind that Heinz Stücke has been riding on a 3 speed with coaster brakes around the world since 1952. And he says 3 speeds is all he needs.

I have a 3speed with coaster brakes fenders and chain guard. One thing that was important for me was having a chain guard, because I could use it in the cooler months and ride to work in my work clothes. Chain guards really make that possible. But I just recently found out that the advantage of a MTB seems to be that the wheels are a little sturdier. I just broke 3 spokes on my 3 speed (and with coaster brakes you don't realize what's going on for a long while).

If you have a MTB with 3x7 or 3x8 gearing you could try just using the front chain rings to change gears. This is not exact but gives you an idea on what it may be like.

Yes the Dutch and Danes seem to like them, and others too. But many of them ride there bikes 1-2 miles to a train station and not much longer than that in very flat terrain.