Commuting bike with the bowed top tube
Its called a "step through" frame, and was initially intended for women wearing skirts.  Notice the skirt guard in the upper-left corner of the rear wheel.

There's no connection with Asia at all, would have originally been English and European.

The curve of the top tube does allow a little more flex, damping out vibrations a bit more. 

As for comfort - it really makes no difference.  There's probably a fraction more side-to-side flex than a high top-tube diamond-frame, but the added damping is a positive.

Really cheap and bomb-proof are likely to entail a lot of weight by using additional metal.  That alone might make for a heavy ride.