Not any more:
- Login authentication requires the phone, even for the web app.
- Card payments require the phone to approve them.
Two of my banks require the phone during the authentication step to login their web apps. Both of them are business accounts.
Recently I had a real problem because my phone screen stopped working (blank screen) though everything else worked. Unfortunately, remote desktop (TeamViewer) works great except for banking apps, where for security reasons it can't grab the screen to relay it. So I phoned one of the banks, and they said there was nothing they could do to authorise access to my account, except get another working phone, which they could then transfer authorisation to.
I had to purchase another phone, then talk with the bank to authorise it, before I could login to the bank account using my laptop to make a payment.
As for card transactions, probably half of my card accounts occasionally bring up a notification on my phone asking me to approve a transaction. So online shopping isn't possible without the phone nearby.
