Saying a certain type of brakes makes you safer is like saying if you put on a jacket while riding a motorcycle your safer. Neither of them make a difference to the way you actually ride or drive, and thats what determines safety.
Unless the rotors are drilled/slotted/significantly bigger your really just paying for the name. Rotors, pads, and calipers are all made from the same materials the only thing that would make a difference in the calipers is the number of pistons if that changes. Brake pads can be gotten anywhere just as nice in my opinion.
"safer" is a loaded and "baggaged" word. It means different things to different people. Each has qualifiers for what it means.
The stock brakes are overkill for tires/rims in the 40 pound range (combined weight). You don't "need" the big brake kit to make it safer in stopping difference. Spend the money on quality tires, as that will make more impact on stopping/braking distance.
On "driving hard" . . . I mean -> how hard one hits the brake pedal. If you hit hard, the unsprung weight and momentum of the wheels come into play.
As is, I can out-brake most other things around me, and out accelerate most too (despite a, relatively, "low" power car).
For "safe," I'd look as much or more into handling and predictability, especially good, grippy tires. That way, you can outmaneuver most problems, rather than relying on brakes and throttle.
Another "concern" with oversized brakes is your own rear-> overbraking the vehicle behind you. A rear tag is a serious safety concern.
Another factor is ABS. It also affects braking distance and negates some of the advantage of big brakes on minimal-fit, light rims. The ABS will kick in and the overall braking distance may not be much less than the smaller brakes with the same rims.
Of course, there are a huge amount of factors when discussing brakes, rims, tires, and suspension.
The BIGGEST difference of all is tires. That is what actually contacts the road and makes the grip. The main factors are compound, for grip, and tread design (how handles the road and conditions).
The second biggest factor is overall wheel wight. The heavier, the more the stopping distance. The reason is the brakes, basically, are causing drag on the rotating mass of the rims. The weight of the vehicle is also pushing the rims forward too.
BUT, the mass of the wheels has a far greater impact than the overall vehicle weight. That is what the brakes are actually stopping.
For example, watch a "donk" stop and see the rims turn red stopping those massive rims. Yet, the actual stopping distance is pretty long.
THAT is where the big brakes make the most difference-> limiting the stopping distance by making heavy wheels stop turning and letting the tires to their thing with grip.
The suspension comes into play more on handling and the balance of braking in a corner or turning situation. As most people "react" before they hit something, turning the wheel to try and miss it.
If the rubber is "lifting" off the road or "sliding" along it instead of gripping, it will extend the stopping distance. The VSC tries to counteract that, but good tire grip best prevents it. A properly set up suspension will also help the grip while turning and braking.
So . . .
Big Brakes, make a bigger difference to "safety" when you have big/heavy rims.
If lighter/stock-weight wheels, the money would be better spent on good, performance tires and suspension tweeking. Those would improve "safety" far more, in my opinion, than the big brakes.
For the sake of continuing this a bit more, lets assume that you DO decide to go with a TRD or big brake kit. Then what? If your like me you eat through pads with relative regularity and any DD or city driver will do the same. Replacement pads will likely be pricier and if you don't do the work yourself your out install fees as well.
Im with you on tires, but personally fighting with the driver aids causes most problems I have. Of course now I know how to actually turn half of them off. Not like it matters too much now though since im back on 2 wheels and the scion is parked
My other ride is an 89/90 Miata, no driver aids. Also, no airbag (anymore) . . .
Driver aids are a WHOLE other issue.
As long as they are predictable, I'm fine with them.
I "learned" to drive in an 87 VW Vanagon, Wolfsburg Ed. (Wolfram Gray). That is the 3rd gen, watercooled Bus. I had that for 7 years, before I got the Miata (on a trade with my father, who bought a new Miata for himself).
It handled great, though rather top heavy and wind-buffeted (6' tall and slab sided). However, it took a while to get to speed and I had to plan ahead to stop.
It's WORSE characteristic was stopping. Yet, I was able to drive it safely, quick, AND avoid a number of accidents.
The "safest" way to drive is to KNOW your vehicle, its pros and cons, and how to AVOID stuff within the parameters of what you have.
THEN, adjust the parameters based on maximum impact for cost.
Big brakes "effectiveness" and impact-vs-price depends on the rims (weight) you run.