"Now what an anti-roll bar does is it allows both tyres to remain on ground during a turn so that we get maximised traction."
Actually just the opposite. The roll bar shifts load from the inside wheel to outside, effectively lifting the inside wheel. With a sufficiently stiff roll bar the inside wheel can be lifted off the ground (Watch most any front wheel drive race event and you will see the inside rear wheels being routinely lifted in the air.)
In less extreme case you have increased the contact pressure on the outer wheel and correspondingly lowered it on the inside. You might expect the net available cornering force to be a wash but it turns out the gain on the outside is less than the loss on the inside, so increasing roll stiffness results in a net loss of available traction. The extreme case is useful to think about as those FWD racers are deliberately tending to oversteer cornering on three wheels.
Of course there are competing effects related to real would suspensions geometry and how the body roll effects keeping the tire flat to the ground, so its not quite so simple. This is why folks typically increase the rear stiffness to reduce understeer, rather than lowering the front stiffness.