No phone number should be a dealbreaker for banking. 99% of the time, you don’t want to talk to a banker. But that 1% of the time can make or break you for months or years.
These start-ups (e.g. Bank Simple, Revolut, et cetera) prey on consumers who have only experienced the 99%. You don’t want to have a 1% event, like fraud, or an issue overseas, or a liquidity crisis, with a service you can’t talk to. (It’s also bad enough when it’s your first time with an issue. You don’t want to be banking with someone who’s (a) never solved that problem before either and (b) not available to talk to.)