Your phone gets stolen so you use your bank card and password to set a new phone number on your account. Your bank card gets stolen so you use your phone and password to get a new bank card.

If someone steals your phone and password and bank card and ability to receive mail at your home address all at once then you're pretty screwed, but you're pretty screwed then regardless, right? That's the level of screwed where somebody else can also get a government ID in your name.

For sufficient amounts or suspicious operations, banks should be in charge of authentification, ie showing up in-person for bank transfers such as a car, showing up and supplying fingerprints if the bank transfer buys a house...

And in fact, for poor people, anything that might engage their entire savings might also benefit from a more advanced identity verification.

For example my stock exchange account just takes a password. It’s a scandal.

Well, you did not mention a password before. With a password, you introduce a new 'security feature' which changes your argument in a non-trivial way.

This might work better than your proposal before.