Softball is a little different than baseball. You almost never need a cutoff on a hit to the outfield unless you are talking 10u or younger.
From what I've seen, I don't agree with this statement. My DD plays 14U B level travel ball. I've seen outfielders try to throw out a runner going home from second over 20 times, and only once did the outfielder actually get the out. Most times, the result of the play is the runner scoring and the batter/runner advancing to second. At 14U B, the outfielders are strong enough to get the ball to home, but are not strong enough to get the ball to home in time to get the out. This might not be true in 14U A or older age groups, but it is certainly true in 14U B.
Given my experience, using a cut-off/relay is always the better approach. The cut-off/relay can then make the decision whether the play at home is a possible out or not. If not, they can then hold the batter/runner at first. Throwing directly home always advances the batter/runner to second.