Resting it against your chest requires that you support it with your left hand. That means you can't move your left hand around, which can be limiting. It's not necessarily lazy, it's just different. One thing it does open up is the possibility of singing and playing the violin at the same time, which clearly is impossible with the classical position.
As for gripping it with your chin/head/shoulder, the combination of shoulder pad, violin body and chinrest should fill just about all the space between the side of your chin and your shoulder. If you can't wedge it in there without arching your neck over or lifting your shoulder, you either need a bigger shoulder rest or your technique's wrong.
The chin rest and shoulder rest aren't "clumsy artificial supports", incidentally, any more than a guitar strap is. It's just what's needed for playing the instrument in a particular posture. There are plenty of "unnatural" things around which give better performance than the "natural" alternatives. ;-)