Or not.
See “The Mayerling suicide pact”. 
That statement is 100% completely inaccurate. There aren’t just a few. There are literally thousands of potentially inhabitable islands in the North American region and tens of thousands world-wide. The Caribbean alone is filled with them and many are for sale. There are about 6000 islands off the coast of Maine alone. Some are inhabited with a tiny population. Others are only inhabited during the summer and still others were once inhabited but aren’t any more. Many of these islands are for sale as well. Large lakes often have sizable islands in them that are privately owned but may be inhabited seasonally or not at all anymore. Of course you have to provide some or all of your own utilities. They don’t just show up on uninhabited islands but you can do it if you really want to.
Here is a tutorial for buying and living on a private island:
Here are some listings for them if you are ready to buy:
Dammit, nothing in my area for less than half a mill…