We anesthetize infants fairly often now[1]. It's still a bit risky, but it's fairly common. It's gotten less risky because we do it a lot and have gotten quite good at it. If we'd never revised the science on infant pain, we never would have even bothered to try. Turns out, it's possible to do it fairly safely.

It's one thing to say, we're not going to use anesthesia because it's too much risk, it's another to say that they don't feel pain at all so let's not worry about it.

[1] http://europepmc.org/abstract/med/26958696