So long as you take sensible precautions I would suggest that emergency avoiding turns can be safely practised in your average training a/c.
Mmmm. I don't know. I think if an emergency avoidance is necessary, then you don't necessarily roll into a steep turn. Instead, it'll be more of a reflex depending on the exact angle with which the other aircraft is closing. Compare it with playing soccer or baseball. Somebody shoots a ball at you and you want to avoid. There is no standard reaction. Instead, you watch the ball, figure out its trajectory and then duck, jump or twist your body to avoid, all in a split second. I think it works the same way in an aircraft. So you either pull into a steep climb, push over into a negative-g pushover or roll the aircraft over in some direction which you think might keep you clear, in a reflex. And you might not stop at 80 degrees, or whatever the limits of "utility category" are.
In any of these scenarios you might end up in an unusual attitude (to put it mildly). You might be pointing straight up and losing airspeed fast, or be inverted. The recovery you need from that is squarely in the aerobatic realm. To practice that safely needs an aerobatics capable aircraft capable of something like -3 to +6 g and temporarily inverted flight. Plus an instructor who knows a bit about aeros, wing root bending effect and the proper way to recover from unusual attitudes.