While I'm still researching the relation of toe and turn in/stability, I think got to the point i could explain it a little. (still not 100% sure if correct)
Before load transfer (due to acceleration of whole car), toe-out gives better turn-in.
This is most apparent on bumpy tracks, with simple, soft suspension (not limited to springs, but general geometry stiffnes - rubber joints etc.). That's because when the wheel go over bump it will bend the suspension and the steering in that wheels direction. When car has toe out it increases the bump loaded wheel slip angle generating a turning (destabilizing) force for the car.
After the car starts to rotate, the horizontal acceleration will shift the load from inside to outside, and as in the picture i posted here earlier (
http://www.racedepartment.com/forum...89-step-1toe-in-out-setup.80590/#post-1615751) toe-out will stabilize the car.
Because soft suspension move slower than steering input, this latter effect will be harder to notice when turning in. (It will be noticeable when operating throttle/brake and driving over big bumps/kerbs with constant steering input).
Now the problem with modern racecars/supercars is that they have 1) advanced suspensions that doesn't bend much over bumps 2) steering that is quite resistant to bumps and(*) 3) lightning fast weight transfer.
This three effects lower the turn-in effect of negative toe, while the really fast weight transfer increases stabilizing effect of negative toe.
This is why i believe on modern cars, and especially on flat tracks it's better to control turn-in with other setup features, and if anything add positive toe on fronts for increased dynamic front end "bite".
(*) I've read about differences in sims vs RL, that for GT racecars you get less feedback from the wheel than in sim actually, and the steering is just rock solid, even over bumps.
I assume turn-in is a moment when car start to respond to driver input, and not steady state when all weight moved to one side. But even then TOE should still have some effect. TOE-OUT will make inside wheel look more towards corner (affecting ackermann). So it will try to steer in tighter radius than outer wheel creating additional slip and more cornering force (inner wheel travels along shorter turn radius than outside wheel so it need to be turned more).
The problem with ackermann is speed, most racecars run almost no ackermann angle at all. Because of 1) large turn radiuses 2) minimal steering even on slow corners (thus minimal ackermann angles) and 3) almost no load on inside wheels meaning that during turn it doesn't really matter in what direction the wheel is pointing. (For example, search for F1 videos with Hamilton when he was racing for McLaren, his inside front was sometimes flying over the track right before apex.)
Also when comparing wheel slip angles of toe-in and toe-out, we cant just look at one tire. Yes the inside wheel will have more slip with toe-out. But the same will be true for outside wheel with toe-in, and it's the outside wheel that has more load, thus the same slip angle will generate more lateral force.