If a cheap camera , in ideal conditions, cant be made to take a good picture then its utterly useless.
A major part of photography is the art, selecting the viewpoint, focusing attention, the whole experience of the image. This is where a good photographer shows. They also pay a lot of attention to light, either shooting at the right time, in the right place, or by supplying their own.
The mechanics of capture dont matter so much, in ideal situations anyhow.
If you want to shoot in low light, or sports, or have shallow DOF or any of those things an SLR really excels at then a P&S is not going to help. Its also not going to let you use filters as easily.
So if your a HCB wannabe then a P&S may be all you need, if your trying to be AA then its unlikely but possible (as he processed a lot and often had infinite depth of field etc).