I´ll give my theory as to why i think Toe out can help the front end initially on turn-in. Probably not a correct theory but here it goes,
Assuming we have a right hand corner, we enter this corner at exactly the same speed with and without Toe out.
If we start with no toe out as a starter, you would turn the wheel let say 90 degrees to make the corner.
With the added Toe out, your left wheel will effectively point out to the left, not much but still.
Wouldn´t this cause you to turn the wheel slightly slightly more to get the left tire in the same angle as the front left without toe as you corner?
If yes, then my theory is that once you gotten the loaded left front tire in the same angle as the non-toe-test you still have a slight advantage due to the right tire pointing slightly more into the turn.
Left side has the most load but the right side tires still have some grip.
So maybe it´s the inside tire that creates this extra feel for turn-in because you have the left side tire in the same angle as the non-toe tire.
Does this make any sense?
The truth will come out...