Goodness, that's rather offhand and completely wrong at lots of levels.
Clearly there a peaks at national and supra-national level. Have a look at some of these for just one example:
http://www.bmreports.com/bsp/b...
Flattening demand would reduce costs of infrastructure that otherwise has to cope with unrestrained peaks; we already do this so it is only a matter of degree and where exactly we do it. Further, allowing demand to follow non-dispatchable load will also help make better use of renewables as well as cope with failure of conventional plant more gracefully.
Also, different parts of the grid will have different problems, eg while the grid may be fine overall at a given moment one substation may be having a torrid time with its much smaller consumer sample, eg that may have a bunch of locals arriving off the same bus or train putting the water for a cuppa, or have a cable fault in one phase, or whatever.
Further, sensible secure schemes will devolve as much as possible of the detailed timing to the appliance so that they cannot all be commanded to 'come on' or 'go off' at once but apply a randomisation algorithm much as Ethernet does for example.
Just because you may have decided up front that there are no good solutions doesn't mean there aren't any. Some of the people that have them know a lot more about stats than you and I both, so can we at least accept that there are entire chunks of maths and computing that have interesting secure distributed randomised algorithms that deal with exactly these sorts of issues all the time?
Rgds
Damon