If the excessive tire wear is from brakes, shouldn't it affect left and right side evenly?
The short answer is both yes and no. When you are driving on a straight road, with no imperfections in the roadsurface and both tires at the same pressure and temperature, braking would affect both tires evenly. But as soon as there is a corner where you brake, uneven roadsurface or different tire pressures, the tires will wear differently.
The long(er) answer:
Basically, what it comes down to is the maximum grip a tire has/can provide. You could visualize this by making a "G-Force"-graph for your tires. When the moving dot is in the middle, all forces on the tire are equal. You can then draw a prefect circle around the center, which is the maximum grip a tire has (i.e.: the maximum force that can be applied to the tire without the tire slipping/losing grip). When the dot moves to the bottom of the graph, the car is accelerating. When the dot is moving to the side, the car is turning to the opposite side.
The tires are used for cornering, accelerating and stopping the car. Sure, the engine produces the power, but the tires transfer the power of the engine to the track, which results in the car accelerating (or moving at constant speed). And yes, the brakes produce the friction (force) necessary to stop the car, but this force is also transfered through the tires to the track. And the steeringwheel makes the fronttires turn, but it is the lateral grip of a tire that makes the car go around a corner.
Whenever there is more force transfered through the tires than there is grip (adhesion) in the tires, the tires lose grip and will slip. A normal street car has most of the time an engine that is not powerful enough to produce more force than the tires can transfer to the street. So there is no wheelspin. A GT3 car has a more powerful engine, which in turn needs better tires. With a GT3 car in 1st gear and full throttle, there will likely be wheelspin. We can visualize this by going back to the G-Force-graph. The force from the enige makes the car accelerate. However, the force produced by the engine is great than the maximum force the tires can transfer to the asphalt, which means the wheel spins. This results in waste of power, slower acceleration and thus losing time. TCS is there to help, but all it does is limiting the engine so there is less wheelspin. Some people are faster with TCS on, some are faster with TCS off. I always race with TCS off, no matter the weather.
When a car turns around a corner, the same rules aply. One cannot go around a left hairpin with 200 km/h. There is more force needed to turn the car with that speed around that corner than the front tires can provide, resulting in understeer. Most racers want to accelerate as soon as possible when exiting a corner. Howerever, when too much throttle is applied when exiting the left hairpin, the dot on the graph moves to the bottomright exceeding the "circle of grip". The rearwheel(s) have to transfer more force to the track then possible, resulting in oversteer.
When braking the same rules apply once more. Too much brakingforce results in the tires locking up (the force exceeds the "circle of grip"), reducing the effectiveness of braking. Ofcourse there is ABS, but all that does is locking and unlocking the brakes like a strobe light. It does not make your car brake harder. When braking while turing, the front and rear tires have to cope with both the lateral forces to make the car turn AND the braking force to slow the car down (front tires moreso than rear tires). Then there is also the effect of weight transfer, which makes the tires on the outside of the corner work harder than the inside tires. This results in uneven workload on tires, thus resulting in different tire wear.
Sugo is a track with lost of stop and go corners and the long sweeping corner at the end of the lap. Therefore the left tires have more work to do, which already results in more tire wear on the left. Couple this with trailbraking and the left tires have even more work to do and probably lock up in the rain. Meanwhile, the right tires have less work to do and probably do not lock up when in a corner.
So to answer your question: it is possible to have both tires wear evenly due to braking, but that is not nearly always the case. To prevent locking up the tires: use lower brake pressures (I am not a fan of simply using higher ABS, since the tires still lock up, albeit in very, very short bursts). This probably also helps with wear due to braking.
Sorry for the long read; I got a bit carried away =P I'll see if I can make some "G-Force-graphs" to visualize the stuff I explained above and make it more readable.