This thread is hilarious, a bunch of people who've never done something, imagining reasons why it can't be done.
My friends and I have been doing this for 20 years without problems. 16 is plenty on a 20" wheel if the rim is even halfway stiff. I've even done 12 out of 36 on wheels that have lasted many years. The spokes do not have to be twice as tight, just tight enough that they don't go slack when at the bottom. In fact you will always get a longer lasting wheel with butted spokes as they can be stretched with less tension.
Radial is not a problem as each pair of webs is only supporting the tension from one spoke.
Skip pairs of holes in the rim, not every other hole. If you don't like the look of radial you can cross when using 16 of 32.
http://bikesmithdesign.com/Paul/16x1wheel.jpg
Another trick for avoiding radial with 18 out of 36 is to use only the trailing spokes on one side and only the leading on the other. Might not work on the rear, though I don't know why, but will build long lasting front wheels.