Some of the posts in this thread confused me. They sounded like some were saying the 2014 Mazda 3 does not have a front sway bar. It does. I can only assume the concerns were actually about replacing the stock rear sway bar with a stiffer unit while leaving the front bar un-changed.
Stiffening the rear roll resistance is a common way to reduce understeer. FWD cars have a very forward biased weight distribution and typically show quite a bit of understeer. Stiffening the rear bar will actually reduce rear traction in corners so that the car is more prone to pivot about it's axis. Understeer can also be reduced by spring rate changes, f/r tire pressure bias and f/r tire size bias.
I had an early mark VW GTI with koni adjustable dampers, ST lowering springs, upper and lower front strut bars, upper rear strut bar, huge front bar and even bigger rear bar. The car was very neutral. It was a full race/auto-x setup. I played with rear tire pressures to fine-tune that rotation. With the mechanical changes in place, adding more tire pressure in the rear reduced the rear contact patch and help promote a neural characteristic. In tight corners the inside rear wheel/tire would actually be off the ground and the car would pivot so easily that you could control the angle with the throttle. Lifting throttle slightly in the curver would shift weight to the front and the rear would start to come around. Adding a little throttle would shift weight to the rear and the rear would come in line. You could take exit ramps at full reverse lock while looking out he diver's side window and controlling the angle of the car with your throttle foot. F'in awesome. The downside was that it was not very forgiving if cooking into a corner too fast. If you lifted, especially too abruptly, you would induce so much oversteer that you were likely to spin and back into the guardrail like a dentist-driven Porsche 911. Understeering cars, while able to reach the same apex speeds, are much more forgiving of entering a corner a bit too fast. Lifting can cause the front to push and this scrubs off speed and uless you have really over-cooked it, your speed drops enough to get front hook-up and make the curve before you run out of road.
With the bars sold for street use with our 3's, the f/r sway bar bias is still very street friendly and designed to keep you in understeer, just less of it than with the OE rear bar.