Define safe. No one has chased me home or run my car off the road, but a lot of people are dealing with a lot of unprovoked violence. And the potential for catastrophic violence has probably never been greater.
But that is not what OP was talking about. The internet has created an environment where people transact business with email addresses and userids. In most cases the business is between strangers. In the interest of convenience, we have created systems that allow users to recover lost passwords with only a little difficulty.
This is a risk and the steps I describe dramatically reduce the liklihood that the vulnerabilities will be exploited. Very worthwhile when I am protecting savings accounts and credit ratings that will put my kids through college.