Many US Financial companies do not allow overseas addresses and might cancel your account.
I just kept a us address and had electronic statements online and email alerts about upcoming payments due.
Occasional snailmail is normally just junk mail credit card offers. The US address I kept is a family members. You can use a u.s. postal e-service to see the scanned mail envelope the night before mail is delivered and tell your family what to keep and what to throw out.
How would you use your Thailand bank account? I have a bank account but I think I have only used it once years ago for the initial visa required immigration deposit. Though admittedly I am lucky because my US bank reimburses the fee for the weekly ATM cash needs. Most credit cards accepted here.