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This must vary a lot by location.

In Singapore, the largest local bank, and three large overseas banks (Citibank, HSBC and Standard Chartered) all require my to be near my phone to login. However, I haven't tried just saying I don't have a phone from the beginning. I know they used to have physical security tokens, perhaps they still would have provided one if I had insisted.

In New Zealand, I've only come across one bank that requires you to provide authentication from your phone (Rabobank), and in Australia I have less experience, but it's not universal either.