Note that the issues you are having won’t just be with 2FA at the bank.
If you get a card from the bank and want to buy anything online from a US website, they’ll want the phone number that’s on the card, and the merchant form may well not allow a number non-US phone number.
At first I kept a toe in the US by keeping a US mailing address and phone number in case I decided after a few years to come back. But there are so many instances where I need a US mailing address and phone number that I’ve continued to pay for my presence in the US over the years and settled here more permanently.
So I pay around $900 a year to maintain a virtual presence in the US. Just the cost of being an expat, you save that in many ways with Mexico’s lower cost of living. Depending on the state of my health, I may eventually have to relocate, whether I really want to or not, and I’ll be happy to have kept phone number, mailing address and bank accounts if that happens. .
So I would recommend keeping your US phone at least initially until you are more settled and then decide. Maybe you can do without it better than me, but don’t burn the bridge until you’re sure you’ll never need it again.