This is a great idea for an ICO. If there was a project you could truly trust it may be a good way for the newbie to protect themselves against rookie mistakes. I'm sure we will see this pop up somewhere along the line.
Insurance to protect bitcoin might apply, but I'm sure not now, because bitcoin currently doesn't get clear status in many countries. Some are legal but many also state that bitcoin is illegal. If this happens, how insurance companies can pay claims because bitcoin is anonymous and peer to peer transactions are clearly unknown to anyone.