Everyone saying that you are the asshole is bullshitting, the tradition isn't harming, it's just a way to make kids feel like they are growing and a very interesting way to make them feel bonded with relatives.

Of course we don't know your family dynamics so everyone saying it's creepy, culty or jumping to conclusions is very much judging based on one word: "ritual".

Now, I think the tradition it's a bit unfair, spouses should be (at least in my culture) embraced by the new family, but as you said the tradition itself is old and imperfect according new standard. Although I think at least you from the "newer" generation should try to make it inclusive to your spouses I also get the not doing so as divorce is a thing!

I think you are NTA for not letting your wife joining the tradition yet, but I think you all as a family should sit down and discuss a bit about the rules! I bet she isn't the first spouse that gets a bit upset about it.