I would not let my kid get a second ear peircing.
I would treat it as a tattoo or nose ring or whatever. They can do that once they are adults, if they want to.
However, I would have no problem with letting my kid get her ears pierced the "regular" way at any age. I know that isn't as common in the US, but where I live, baby girls get their ears pierced in the hospital after they are born. That's the norm, I'm not sure they even ask you if you want to do it. They probably do but it's so rare to find a baby girl that does not have her ears pierced that I wonder if they ask.
I don't know what I will do if/when I have a daughter. On the one hand I would want to let her have a choice (even though most women/girls want to have their ears pierced) and I wouldn't want to do that right after they are born for sure. On the other hand, if they are anything like me, and I don't do it when they are babies, they will never ever get it done, no matter how bad they want it.
If I didn't have my ears pierced, I would NOT, no way no how, want to go through that due to anxiety about these kinds of things. I think I would have to be sedated to do it and while it healed too. So there can be advantages and disavantages to both choices.
But for sure no on the second piercing.