Are all immigration offices in Chiang Mai able to provide the same services for non-O visa holders?

It is a Certificate of Residence you'll get - you complete a form requesting one and select the "to open bank account" tickbox

In all immigration offices there are not two officers who administer the rules the same! TiT!

You are a Non-O holder so not sure why a letter from immigration would be required, other than a lack of understanding of the requirements by the bank? Are there other issues or requirements that they have? Try another branch or bank. SCB were asking for a Yellow Book from me (which I recently have) as a requirement. K-Bank seem to have less requirements.

And your phone number registered to your passport, for the bank.

You won't get a letter from immigration saying it's ok to open a bank account. All you'll get is a certificate of residency which does nothing but confirm your address. You take this to the bank, but the bank will still need your passport with non-immigrant visa and probably a 12-month lease before they'll open an account

I'm not completely sure of what your question is.

Every "main" immigration office can provide all immigration services. Branch/Secondary offices do not always offer the same level of service as the main office in a province, if that province even has any secondary offices.

The main office near the airport can do everything.

You are talking about a residence certificate. Yes Chiang Mai immigration at the airport offers residence certificates. These do not tell banks they can open accounts for you. They just verify your address, and say that the purpose is for opening a bank account if that's the reason you request it. Whether a bank opens an account for you or not is up to the manager and staff of any branch that you visit.