3 year ARC for my wife, how to get it upon entry?

Thanks for the responses,
What are the advantages of having a JFRV vs ARC? we want to be able to travel in and out of Taiwan to visit places like japan or china. She only has a single entry visitor visa. This is the best visa we could get for her.
Our marriage is officially registered in Taoyuan Taiwan where I have my Residence registry, I did the marriage application through the TECO here in US.

I read too that its unlikely they will give the 3 year, but anyone know why they don’t give initially and why they give after the first year?

thanks in advance