Even though the idea of opening an offshore bank account from your living room may sound appealing, things are not as easy as they seem and they are becoming even harder.
Given that the bank employees don't see you in person, you will have to file a significant amount of documentation, which can take more time and effort than actually traveling to the place where you want to open the account.
It also has to do a lot with the banks' quality and level of the jurisdiction of the countries which are open to remote bank account opening, so think wisely.