I don't know how the procedure looks like in wherever-you-are but in EU phone number is required to either have a call from agent or to receive verification codes from text messages if bank you've pick offers opening an account on your own. Either way, bank gets all your personal data - you are not anonymous for them.

And the SIM registration requirement in nearly every EU country exists for 10 years now - in my case it was as simple as replying with code to operator's message because they had my personal information already for over a decade. There was a grace period after which unregistered SIM cards become dead - the requirement was dubious but you had to comply in order to call, text. There were "solutions" I've bumped on in depths of the Internet but neither felt serious nor safe.