"The paper is observing that if the peak was lower, by having a little more randomness in the demand, there would be fewer problems supplying the overall demand as it would be spread over a greater period of time."
That's true, but they are framing it like this is a revelation to the power companies. The power companies already know. They may not know precisely *why* it's happening, but they know it's happening and can account for it. On the other hand, as you say, it could be spread out more but that's really a public education thing, which the power companies might like to get involved in, but I suspect it would, in reality, end up with most[*] people thinking, "ah fuck it, I'll just add 'n' minutes to the timer". Most people will almost certainly add 1-5 mins, not actually making much of a difference. A real solution would be for "smart" home devices such as thermostats actually be smart and talk to others in the neighbourhood or the power company and negotiate a time around about when the user wants it on and come on sooner or later by some minutes.
[*] "most" being of those who even give it a thought, that is. There'll be plenty who think it doesn't apply to them or don't care, or assume others will do something. And, being the USA, there'll be a certain percentage who say something along the lines of "Muh FREEDOM!!! BigGuv/BigCorp ain't telling ME when I can turn on muh heat!!!"