In many countries it's already impossible to use just the web for banking. They either make you install rootkits on your computer or move you to their mobile apps
Many countries have only three or four full banks (the kind that can give you a Visa or Mastercard bank card, let you send and receive transfers, etc.), and all of them are making the same moves.
I am aware that some banks require apps on "certified" phones, but I haven't heard of rootkits on PCs, yet. Do you have an example of that?