Forget the idea, that's enough to connect points A and B by a piece of wire to produce a connection fullfilling all needs of a digital circuit. You totally overlook, that wave packets are actually running through transmission lines with such a digital circuit. And you need the solid ground plane to guide this wave packets. If you omit the solid ground plane, then you get lots of ringing and ground bounce, which will result in a total erosion of noise margins.
I echoed that sentiment in an earlier post in this thread http://www.8052.com/forum/read.phtml?id=134778.

I think to recall some time (years?) ago there was a post here? "look at my magnificientn single sided board - (almost?) no jumpers" followed by "why does it not work" Traces almost ran around the board 3 times.

Sure, but he does not want to 'design' he wants to 'test' and when the 'test' fails he does not relate that to the lack of 'design' but invariably to something else.

Erik