So, I am assuming you want to use your US credit card in your country of residence and pay off the credit card balance with the accounts you have in the U.S. Makes sense to me. I am an American living abroad and do the same thing with larger purchases using a credit card I got when I still lived in the U.S.
I recently asked my U.S. based bank about a new credit card, but they told me I must have an address in the U.S. for at least 90 days before I can apply for a new credit card.
Also, a fico score is tied to a U.S. social security number or ITIN. If you don’t have a SSN, you probably have an ITIN. An ITIN looks a lot like a social security number but is typically assigned for non-resident aliens (foreigners not living in the U.S) or under age immigrants on temporary visas.
Please note that the cost savings you are thinking about might not actually be real. Credit card companies might use exchange rates that essentially have the 2% cost baked in.
Finally, as others have suggested, you might want to use a Wise account. I have a Wise account denominated in USD with a US routing and account number, which means ACH transfers. You can get debit card tied to the Wise account. They do not charge international transaction fees and offer decent exchange rates. Be careful about carrying large balances in your wise account though, there have been some stoep from people whose accounts were frozen and who had a really hard time getting them unfrozen.
This is what broke my previous relationship. We met in my country. She went back to hers. We kept flirting. Started for real in a third country, things were great. Moved to her country. She slipped back into all her old routines and friend circle. She could not understand that I as a foreigner in her home country might have cultural adjustment issues, language issues, etc. I wanted to move to a new third country. She didn’t, she thought her country was the best place in the world. Eventually it all fell apart.