Sufficient, but not necessary. “No one” is too strong—the general recommendation in the conclusion can still hold as long as people tend to have a common preference about where their estates go. Also, the author only has to assume that people don’t want distant relatives they’ve never met to have a greater legal right to the estate than their friends do. It’s fine if some people want a charity, or close relatives they haven’t met, to have a greater legal right than anyone else.

The concept of who is “deserving” has no part in the reasoning of the argument. Although the author assumes that people have preferences about how the estate is distributed, this doesn’t imply that the estate should be limited to people who are “deserving.”

The concept of “unjust” has no part in the reasoning of this argument. Although the author assumes that people have preferences about how the estate is distributed, this doesn’t imply that certain distributions are “unjust.”

Necessary, because if this were not true — if people ARE generally indifferent about how their estates are distributed — then the premise no longer provides a reason to think anyone should have a will. If people generally don’t care about who their estates go to, then why should the distant relatives vs. friends situation lead one to want a will?

Not necessary, because under current law, one’s distant relatives have a greater legal right than one’s beloved friends do. The author assumes that people generally want their friends to have a greater legal right, but that isn’t true under current law.