That's not a bad solution. It would certainly correct the skewed influence of Iowa and New Hampshire. Reminds me of an old joke: A reporter asks a New Hampshire resident which candidate he supports for president. He answers, "Well, I suppose I can't rightly say. I haven't even met some of them yet."
The best thing of all is that it would screw over the professional pundits and “advisors” who are hyperspecialized at winning three or four specific states. Whatever would they do without “conventional received wisdom” to cling to. Imagine if Alaska, Maine, Wisconson, Louisiana, and West Virginia were suddenly the first to vote. Or NY, CA, TX, MI, and VA.