It takes a lot more than a few seconds to bring an elephant down with tranquilizers.
I did a little more research on the question of alternative weapons that incapacitate. I'm not the first person to raise the question. There are tranquilizers that can instantly incapacitate. However, the main problem in using them in law enforcement is that one size does not fit all. A tranquilizer dose and even a taser setting high enough to kill a 120 lb person might not even phase a 300 lb person. This seems to be the main obstacle in using a tranquilizer as a weapon against perps -- proper and effective dosage.