You really seem to have misapplied a lot of your safety lessons. Cars and motorcycles and bikes all have different safety strengths and weaknesses.

Bike has more visibility than a car, so looking both ways before an intersection is fine.

Bike is often right hooked, so waiting on the right is a less safe method for handling red-light runers.

Cars get rear ended. When it happens at a red light, it's usually a pain because the front car can't get out of the way. A bike can. It's maneuverable. More so than a motorcycle.

Instead, your solution is to place yourself in a less safe spot.