Don't like that. I'm of the "if you're going to do something important, do it on your PC" generation. I do not want a future where I lose my phone and I can no longer access my bank.
They won't find a solution to your problem, when one is obvious: buy a phone.
They'll find a solution to their problem, which is you: apologize for losing you as a customer, and express a hope that you'll consider them again after you've bought a phone.
There can be laws like the right to have a bank account, that might say your bank can't require you to have anything they don't provide you with for free. In some places.
We need to act now, while there are still service providers that don't require a phone. If my bank said they wouldn't do business with me unless I used a phone and an app, I would immediately take my business and all my accounts to a different bank. Banks have no moat. You can pretty easily move accounts to a different one or to a credit union who won't abuse you.