I don't think you should force a child to see something they may not want to or be ready for. I was interested in animals and pets as a child, but like I said, if I saw something - anything - die, I would start crying, and I can still remember some traumatizing experiences. I would not subject anyone to that, adult or child.
At 3 years old a child should not have the responsibility to take care of animals, just because they are learning about it. It's like anything. Take it in steps, don't shove it down their throats.

Watching an animal die is not the same as scooping poop. Compare it all you want, it is not the same.
I agree that children should be empowered. So empower them to make a decision about what they want. And if they want to watch you feed live, then there you go. If they haven't shown interest, that's another story. There is no way to know what kind of adverse effects you can cause.
Yes, it may just be a little mouse or rat, and it may be a common thing in your household. And I doubt every little child who sees a live feeding will be bothered. But you never know, and I wouldn't want to be the reason my child grows up either afraid of snakes, upset at me, or worse - it does happen.