A couple other reasons we store tails out...
1) The print-through on a tape stored heads-out is more noticeable because it presents as pre-delay. With tails-out its less noticeable as a natural echo.
2) Its best to fast wind a stored tape before use. Storing tails-out makes this necessary, but easy. Simply pop the reel on the right side and rewind. In fact its best to fast wind a new tape, so start with a new reel of tape face down on the right hub, then rewind the tape to an empty reel. After rewind once the new reel is empty, turn it label side up before recording.
And that is correct that the way to get to tails-out is at spool or play speeds, for a nice even pack.