Except that running as an independent is a HUMONGOUS pain in the ass. Even more of a pain in the ass than running for president is already. The reason for this is that each state has its own rules and deadlines for how an independent can get on the ballot. Simply put, if you lose the nomination of your party and try to run as an independent, you've already missed out on a bunch of states. It might even be enough states to make it impossible to win.