This isn't relevant for your example as in your example, you are entering the freeway on-ramp at a low speed and accelerating throughout the entire corner. Navigating a corner at highest possible speed means you're arriving at the corner at a high speed and must decelerate in order to make the corner.
It's not immediately clear to me why you would use gas and brake at the same time in an automatic transmission vehicle. The only reason I can think of would be to keep the revs of the engine in the powerband and prevent the car from downshifting so that you can immediately have full power when you accelerate out of the apex. In a manual transmission vehicle, there's a technique called heel-and-toe where you blip the gas pedal with your heel to rev-match the engine on your downshift while braking with your toe and depressing the clutch with your left foot, but you're never introducing force to the front wheels that would counter the force of the brakes.
When cornering hard, because of weight transfer, the inner wheel loses almost all traction, which makes it impossible to send any torque to it without wheel spin. This means that you can't really accelerate out of a sharp turn with an open-diff vehicle, because an open diff always sends the same torque to both wheels, i.e. if the inner wheel spins without much resistance, that resistance equals the torque sent to the outer wheel.
A poor-man's-LSD-solution to this is applying a bit of brakes while also giving it a lot of gas. The brakes prevent the inner wheel from spinning freely and add artificial resistance, which increases the torque available at the outer wheel.
Ideally you'd only want to apply the brake on the inner wheel, which is what some cars actually do automatically as a fake-LSD solution, but applying both and wasting engine power is better than nothing.
Why do you need the brakes? The nearest freeway on ramp to my home is unusually short, and it's a 270 degree turn. I've had to get very good at getting my vehicle to accelerate as quickly as possible around that curve so that I can merge safely when the on ramp ends.
I don't need the brakes to do that, in fact the front brakes in most vehicles are usually much stronger and the braking bias is usually weighted greatly in favor of the front brakes. So again, I really don't know why you need the brake, especially in a front wheel drive car... you're just fighting the engine and the brakes can usually win that fight (except for in high powered rear wheel drive cars where the rear brakes are weak and the engine can overpower them).