You do not need to have a perm visa to open a bank account in Mexico, the only one that requires it is Banamex, all other are temp visa, CiBanco, Bancomer, Santander and Banorte, all others as Inbursa BajioBanco, Azteca, Coppel Banco, etc. I do not know as they are very small entities and seldom do any international transactions that I know.
IMHO all Mexican banks are a mess, for a simple transaction as deposit or withdrawal they have to jump from software to software to complete it and takes 30 minutes to do something that should take less than 3 minutes, in and out, Bancomer was always bad in Puerto Penasco, hell even in Hermosillo which is a city with a million-plus people in eat.
In top of that my account was open in HMO and I moved to Guaymas in order to activate my card I had to go back to HMO because the branches in different cities in Mexico are not linked to each other, talk about convenience!!