The on-track duels could be epic... I think certain complexes would become crazy fast tho. The Lesmos, Maggots/Becketts, and lots more of Monaco would be able to be taken flat out...
No matter how you slice and dice it, the fastest way through a corner is the straightest path. When racing you have to prioritize corners and sometimes give up speed to set up the next corner. The most important corner is a corner that leads onto a straight; a corner that leads to another corner that leads to a straight might not be taken by the fastest line, since the exit would not set you up for the corner leading to the straight, if you get my drift. Having four corner control of power to wheels would not change this at all; it might make it easier to turn the car on entry, but the fact is there is only so much grip available and to go off line and take some path that makes you keep turning the car when another line allows acceleration is going to be the slower line.
Imagine this: the fastest way through corner A means you end up on the left hand side of the track at exit, but the next corner, corner B that leads onto the long straight, is best done by entering the corner from the right hand edge of the track to achieve the least turning radius and hence higher speed. If you are to the left you have to keep turning the car instead of accelerating. Look at some basic driving books for more examples; it's pretty simple. There is a fastest way around the track.....and that's the straightest way.