Your story sounds a bit strange. If all you want is access to your money anywhere in the world, you can just use the debit card for your bank as long as it has a cirrus or interac symbol on the back of it. The exchange rates from ATMs are about as good as you can get and the fees are minimal or nothing to use the ATM.

Getting an offshore account really isnt worth it unless you have over 100 000 dollars to put in. HSBC may not even open an account unless you have this minimum amount. Even if you do have that, offshore banks charge a lot of fees for money transfers, etc. Also, you have to keep your money tied up in the account because you cannot go below the 100 000 dollar limit without getting hit by more fees.

Furthermore, it is not wise to be far from your money. Offshore accounts generally do not insure your deposit. So, if that bank goes under, you are screwed. This is in contrast to domestic banks that would insure your deposit because it is backed by the government.

The only reason to have an offshore account would be because you want to hide a large sum of money/investments from your government, business partner, wife, etc. You might also use it if you were a citizen of a country like Nigeria or something that is unstable and not trustworthy.

The only other reason I can think of is if you were a true expat who was unable to open a bank account/credit card in your home country and in the country in which you are residing.

Personally, I just use my home bank account because it is in a stable country. My QNB account is used just for local payments/credit cards. I get cash for day to day living from home via the ATM here in Doha. If I need a large amount, I get it wired from home to my QNB account.