It's funny, though, how everyone already takes similar trade-offs all the time. E.g., we're trading a high risk of dying a violent death at the hands (or claws) of enemies and predators (life in the primeval savanna) for a lower risk of dying of obesity, diabetes, and so on (modern "civilized" life).
That bleeding can cause other problems like anemia, and aspirin can also cause ulcers, which besides the discomfort, can become a serious medical emergency.
This is truly a balancing act, and we really don't know enough to balance it for generally-healthy people at large.